This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common...This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.展开更多
In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems wi...In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.展开更多
This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nomina...This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.展开更多
This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the exp...This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference （Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20（12）, 4105-4109 （2010））, a nonlinear feedback gain is needed to generate chaotic dy- namics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the con- troller is constructed by Russell＇s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller.展开更多
The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedbac...The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.展开更多
A two-layer switching architecture and a two-layer switching rule for stabilization of switched linear control systems are proposed, under which the mismatched switching between switched systems and their candidate hy...A two-layer switching architecture and a two-layer switching rule for stabilization of switched linear control systems are proposed, under which the mismatched switching between switched systems and their candidate hybrid controllers can be allowed. In the low layer, a state-dependent switching rule with a dwell time constraint to exponentially stabilize switched linear systems is given; in the high layer, supervisory conditions on the mismatched switching frequency and the mismatched switching ratio are presented, under which the closed-loop switched system is still exponentially stable in case of the candidate controller switches delay with respect to the subsystems. Different from the traditional switching rule, the two-layer switching architecture and switching rule have robustness, which in some extend permit mismatched switching between switched subsystems and their candidate controllers.展开更多
This work addresses observer design for the general class of quasi-reversible discrete-time switched linear systems.Under the mild assumption that the switched system is observable,we present constructive approaches t...This work addresses observer design for the general class of quasi-reversible discrete-time switched linear systems.Under the mild assumption that the switched system is observable,we present constructive approaches to design state observers to estimate the state.Two types of observers are designed:one is with full order and the other is with reduced order,both could reconstruct the system state in finite times.A numerical example is presented to illustrate the effectiveness of the proposed approaches.展开更多
The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant s...The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is （QLFs） is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.展开更多
This paper deals with the problem of optimal fault detection filter （FDF） design for a class of discrete-time switched linear systems under arbitrary switching. By using an observer-based FDF as a residual generator...This paper deals with the problem of optimal fault detection filter （FDF） design for a class of discrete-time switched linear systems under arbitrary switching. By using an observer-based FDF as a residual generator, the design of the FDF is formulated into an optimization problem through maximizing the H_/H∞ or H∞/H∞ performance index. With the aid of an operator optimization method, it is shown that a mode-dependent unified optimal solution can be derived by solving a coupled Riccati equation. A numerical example is given to show the effectiveness of the proposed method.展开更多
This paper addresses the cooperative output regulation problem of a class of multi-agent systems （MASs）. Each agent is a switched linear system. We propose an agent-dependent multiple Lyapunov function （MLF） appro...This paper addresses the cooperative output regulation problem of a class of multi-agent systems （MASs）. Each agent is a switched linear system. We propose an agent-dependent multiple Lyapunov function （MLF） approach to design the switching law for each switched agent. The distributed controller for each agent is constructed based on a dynamic compensator. A sufficient condition for the solvability of the output regulation problem of switched agent networks is presented by distributed controllers and agent-dependent multiple Lyapunov function approach. Finally, simulation results demonstrate the effectiveness of our theory.展开更多
In this paper,the authors propose an approach to properly aggregate a reversible discretetime switched linear system and prove that,for any n-dimensional exponentially stabilizable switched system,the authors could de...In this paper,the authors propose an approach to properly aggregate a reversible discretetime switched linear system and prove that,for any n-dimensional exponentially stabilizable switched system,the authors could design up to n linear gain matrices,such that the extended system is also exponentially stabilizable as a switched autonomous system.By utilizing the pathwise state feedback switching strategy of the switched autonomous system,the original system is aggregated into a piecewise linear system that is step-wise norm contractive and exponentially stable.The authors also develop a robust switching design mechanism that simultaneously achieves exponential stability,structural stability,and input-to-state stability for the closed-loop system.A numerical example is presented to demonstrate the effectiveness of the proposed design scheme.展开更多
Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in ...Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in system analysis and synthesis.Nevertheless,numerous difficulties and challenges are also encountered due to the reciprocal effects of switching signals and scheduling parameters in the analysis and synthesis of switched LPV systems.In this paper,the standard description and specific characteristics of switched LPV systems are first introduced.Then,the main methodologies are proposed in the literature to cope with stability and performance analysis,control synthesis,as well as fault diagnosis and fault-tolerant control issues,and the typical applications in various fields are surveyed.Finally,several key open problems and current research activities are also discussed to elucidate the potential research directions in the future.展开更多
Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitr...Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(i)instability with stable matrices and(ii)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(i)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ii)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.展开更多
In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by ...In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.展开更多
Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature...Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature,the important role of switched and impulsive time sequence is considered.Applying the relevant geometric theory of matrix,a necessary and sufficient criterion for the controllability is firstly developed to judge when the controllability of such systems is affected by switched and impulsive time sequence.Furthermore,we further obtain a sufficient controllability condition that can be used to verify the controllability of such systems regardless of the switched and impulsive time sequence.Finally,a numerical example is given to verify the obtained theoretical results.展开更多
In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of...In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.展开更多
The stabilization of switched linear systems with constrained inputs （SLSCI） is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time （MDT） to stabi...The stabilization of switched linear systems with constrained inputs （SLSCI） is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time （MDT） to stabilized the system. First, for each subsystem with constrained inputs, a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system＇s states lie inside this set. Then, by constructing a quadratic Lyapunov function for each closed-loop subsystem, an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system.展开更多
The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability condition...The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.展开更多
This paper studies the problem of robust H∞ output feedback controller via state-reset for linear uncertain discrete-time switched systems. Using multiple Lyapunov functions,we address an output feedback controller u...This paper studies the problem of robust H∞ output feedback controller via state-reset for linear uncertain discrete-time switched systems. Using multiple Lyapunov functions,we address an output feedback controller under arbitrary switching signals,in which an H∞ performance is required. The condition is shown in the form of linear matrix inequalities (LMI). Finally,a numerical example shows the feasibility of the designed controller and illustrates that the new sufficient condition has lower conservation and more optimized H∞ tfperformance.展开更多
For switched linear system with colored measurement noises,the identification difficulties of this system are that there exist unknown switching information,unknown middle variables and noise terms in the information ...For switched linear system with colored measurement noises,the identification difficulties of this system are that there exist unknown switching information,unknown middle variables and noise terms in the information vector.For the mentioned issues,the fuzzy clustering and the multi-innovation recursive identification algorithm are used to deal with these problems.Firstly,the mode detection is transformed into the detection of membership degree values confirmed by the fuzzy clustering method,and the problem of mode detection is solved by judgment and decision of the fuzzy membership values.Moreover,the multi-innovation recursive identification algorithm based on the generalized auxiliary model is proposed to estimate the parameters of the switched linear system with colored noises.Finally,the effectiveness of the proposed method is verified by the results of the simulation example.展开更多
基金supported by National Natural Science Foundation of China(No.61374065)the Research Fund for the Taishan Scholar Project of Shandong Province
文摘This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.
基金This work was supported by the National Natural Science Foundation of China(No.60343001, 60221301) and the Foundation of Harbin EngineeringUniversity.
文摘In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.
基金supported in part by the National Defense Basic Scientific Research Program of China(JCKY2018603C015)Cultivation Plan of Major Research Program of Harbin Institute of Technology(ZDXMPY20180101)
文摘This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.
基金supported by the National Natural Science Foundation of China(Nos.11071262,11101440,and 61263011)
文摘This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference （Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20（12）, 4105-4109 （2010））, a nonlinear feedback gain is needed to generate chaotic dy- namics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the con- troller is constructed by Russell＇s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller.
文摘The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.
基金supported by the National Natural Science Foundation of China(No.61233002)the Fundamental Research Funds for the Central Universities(No.N120404019)
文摘A two-layer switching architecture and a two-layer switching rule for stabilization of switched linear control systems are proposed, under which the mismatched switching between switched systems and their candidate hybrid controllers can be allowed. In the low layer, a state-dependent switching rule with a dwell time constraint to exponentially stabilize switched linear systems is given; in the high layer, supervisory conditions on the mismatched switching frequency and the mismatched switching ratio are presented, under which the closed-loop switched system is still exponentially stable in case of the candidate controller switches delay with respect to the subsystems. Different from the traditional switching rule, the two-layer switching architecture and switching rule have robustness, which in some extend permit mismatched switching between switched subsystems and their candidate controllers.
基金supported by the National Key R&D Program of China(2018YFA0703800)the Natural Science Foundation of Shandong Province(ZR2020ZD26).
文摘This work addresses observer design for the general class of quasi-reversible discrete-time switched linear systems.Under the mild assumption that the switched system is observable,we present constructive approaches to design state observers to estimate the state.Two types of observers are designed:one is with full order and the other is with reduced order,both could reconstruct the system state in finite times.A numerical example is presented to illustrate the effectiveness of the proposed approaches.
基金Supported partly by National Natural Science Foundation of PRC (No. 60343001, 60274010, 66221301 and 60334040)
文摘The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is （QLFs） is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.
基金supported by the National Natural Science Foundation of China(6117412161121003+2 种基金61203083)the Research Fund for the Doctoral Program of Higher Education of Chinathe Doctoral Foundation of University of Jinan(XBS1242)
文摘This paper deals with the problem of optimal fault detection filter （FDF） design for a class of discrete-time switched linear systems under arbitrary switching. By using an observer-based FDF as a residual generator, the design of the FDF is formulated into an optimization problem through maximizing the H_/H∞ or H∞/H∞ performance index. With the aid of an operator optimization method, it is shown that a mode-dependent unified optimal solution can be derived by solving a coupled Riccati equation. A numerical example is given to show the effectiveness of the proposed method.
基金supported by National Natural Science Foundation of China(Nos.61304058 and 61233002)IAPI Fundamental Research Funds(No.2013ZCX03-01)General Project of Scientific Research of the Education Department of Liaoning Province(No.L2015547)
文摘This paper addresses the cooperative output regulation problem of a class of multi-agent systems （MASs）. Each agent is a switched linear system. We propose an agent-dependent multiple Lyapunov function （MLF） approach to design the switching law for each switched agent. The distributed controller for each agent is constructed based on a dynamic compensator. A sufficient condition for the solvability of the output regulation problem of switched agent networks is presented by distributed controllers and agent-dependent multiple Lyapunov function approach. Finally, simulation results demonstrate the effectiveness of our theory.
基金supported by the National Natural Science Foundation of China under Grant No.62373228。
文摘In this paper,the authors propose an approach to properly aggregate a reversible discretetime switched linear system and prove that,for any n-dimensional exponentially stabilizable switched system,the authors could design up to n linear gain matrices,such that the extended system is also exponentially stabilizable as a switched autonomous system.By utilizing the pathwise state feedback switching strategy of the switched autonomous system,the original system is aggregated into a piecewise linear system that is step-wise norm contractive and exponentially stable.The authors also develop a robust switching design mechanism that simultaneously achieves exponential stability,structural stability,and input-to-state stability for the closed-loop system.A numerical example is presented to demonstrate the effectiveness of the proposed design scheme.
基金supported in part by the National Natural Science Foundation of China(62222310,61973131,62473379)the National Key Research and Develepment Program of China(2024YFB3310701)+1 种基金the Research Fund for the Taishan Scholar Project of Shandong Province of China,the Major Basic Research of Natural Science Foundation of Shandong Province(ZR2024ZD38,ZR2022ZD34)the Japan Society for the Promotion of Science(21K04129).
文摘Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in system analysis and synthesis.Nevertheless,numerous difficulties and challenges are also encountered due to the reciprocal effects of switching signals and scheduling parameters in the analysis and synthesis of switched LPV systems.In this paper,the standard description and specific characteristics of switched LPV systems are first introduced.Then,the main methodologies are proposed in the literature to cope with stability and performance analysis,control synthesis,as well as fault diagnosis and fault-tolerant control issues,and the typical applications in various fields are surveyed.Finally,several key open problems and current research activities are also discussed to elucidate the potential research directions in the future.
文摘Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(i)instability with stable matrices and(ii)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(i)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ii)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.
文摘In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.
基金supported in part by the National Natural Science Foundation of China(62322311,62303162,62233007,62203157)the Technology Development Program of Henan Province(242102211052).
文摘Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature,the important role of switched and impulsive time sequence is considered.Applying the relevant geometric theory of matrix,a necessary and sufficient criterion for the controllability is firstly developed to judge when the controllability of such systems is affected by switched and impulsive time sequence.Furthermore,we further obtain a sufficient controllability condition that can be used to verify the controllability of such systems regardless of the switched and impulsive time sequence.Finally,a numerical example is given to verify the obtained theoretical results.
基金supported by the National Key Basic Research Program(973 Plan)under Grant No.2014CB845302the National Natural Science Foundation of China under Grant No.61273121
文摘In this paper,an approach of square coordinate transformation is proposed to approximate the spectral abscissa for continuous-time switched linear systems.By applying elementary transformations iteratively,a series of minimums of least μ1 matrix set measures are obtained,which are utilized to approximate the spectral abscissa of the switched system.The approach is developed into tractable numerical algorithms that provide upper bound estimates of the spectral abscissa.Numerical simulations show the effectiveness of the proposed method.
基金supported by the National Nature Science Foundation of China under Grant Nos:60674022, 60736022,and 62821091
文摘The stabilization of switched linear systems with constrained inputs （SLSCI） is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time （MDT） to stabilized the system. First, for each subsystem with constrained inputs, a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system＇s states lie inside this set. Then, by constructing a quadratic Lyapunov function for each closed-loop subsystem, an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system.
基金the National Natural Science Foundation of China (69874008).
文摘The stability and stabilization of a class of linear switched time-varying delay systems are investigated. A piecewise quadratic Lyapunov function （PWQLF） is constructed and is used to obtain the stability conditions based on the linear matrix inequalities （LMIs）. The stabilizing controller for this class of system is then designed and the solution of the desired controller can be obtained by a cone complementary linearization algorithm. Numerical examples are provided to illustrate the less conservativeness of the new stability and the validity of the controller design procedures.
文摘This paper studies the problem of robust H∞ output feedback controller via state-reset for linear uncertain discrete-time switched systems. Using multiple Lyapunov functions,we address an output feedback controller under arbitrary switching signals,in which an H∞ performance is required. The condition is shown in the form of linear matrix inequalities (LMI). Finally,a numerical example shows the feasibility of the designed controller and illustrates that the new sufficient condition has lower conservation and more optimized H∞ tfperformance.
基金supported by the National Natural Science Foundation of China(61863034)
文摘For switched linear system with colored measurement noises,the identification difficulties of this system are that there exist unknown switching information,unknown middle variables and noise terms in the information vector.For the mentioned issues,the fuzzy clustering and the multi-innovation recursive identification algorithm are used to deal with these problems.Firstly,the mode detection is transformed into the detection of membership degree values confirmed by the fuzzy clustering method,and the problem of mode detection is solved by judgment and decision of the fuzzy membership values.Moreover,the multi-innovation recursive identification algorithm based on the generalized auxiliary model is proposed to estimate the parameters of the switched linear system with colored noises.Finally,the effectiveness of the proposed method is verified by the results of the simulation example.
