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
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
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
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
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
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
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
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
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
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
This paper focuses on the H_∞ model reference tracking control for a switched linear parameter-varying(LPV)model representing an aero-engine. The switched LPV aeroengine model is built based on a family of linearized...This paper focuses on the H_∞ model reference tracking control for a switched linear parameter-varying(LPV)model representing an aero-engine. The switched LPV aeroengine model is built based on a family of linearized models.Multiple parameter-dependent Lyapunov functions technique is used to design a tracking control law for the desirable H_∞ tracking performance. A control synthesis condition is formulated in terms of the solvability of a matrix optimization problem.Simulation result on the aero-engine model shows the feasibility and validity of the switching tracking control scheme.展开更多
For linear switched system with both parameter uncertainties and time delay, a delay-dependent sufficient condition for the existence of a new robust H∞ feedback controller was formulated in nonlinear matrix inequali...For linear switched system with both parameter uncertainties and time delay, a delay-dependent sufficient condition for the existence of a new robust H∞ feedback controller was formulated in nonlinear matrix inequalities solvable by an LMI-based iterative algorithm. Compared with the conventional state-feedback controller, the proposed controller can achieve better robust control performance since the delayed state is utilized as additional feedback information and the parameters of the proposed controllers are changed synchronously with the dynamical characteristic of the system. This design method was also extended to the case where only delayed state is available for the controller. The example of balancing an inverted pendulum on a cart demonstrates the effectiveness and applicability of the proposed design methods.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
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 issues of event-triggered exponential L1 filtering are studied for a class of networked linear switched systems.An event-triggered mechanism is proposed to enhance resource utilization in transmission,and save the...The issues of event-triggered exponential L1 filtering are studied for a class of networked linear switched systems.An event-triggered mechanism is proposed to enhance resource utilization in transmission,and save the communication cost of systems as well.Then,the filtering error system is reconstructed as a switched delay system with bounded disturbance through the input delay system approach.By resorting to the Lyapunov-Krasovskii functional approach and the average dwell time(ADT)technique,some interesting results are derived to guarantee the exponential stability with a prescribed L1 disturbance rejection level.Further,an event-triggered exponential L1 filter is designed via solving a set of feasible linear matrix inequalities(LMIs).Finally,the efficiency of the proposed results is verified through a numerical example and a PWM-driven boost converter circuit system.展开更多
This paper investigates the state-tracking control problem in conversion mode of a tilt-rotor aircraft with a switching modeling method and a smooth interpolation technique.Based on the nonlinear model of the conversi...This paper investigates the state-tracking control problem in conversion mode of a tilt-rotor aircraft with a switching modeling method and a smooth interpolation technique.Based on the nonlinear model of the conversion mode,a switched linear model is developed by using the Jacobian linearization method and designing the switching signal based on the mast angle.Furthermore,an ℋ_(∞) state-tracking control scheme is designed to deal with the conversion mode control issue.Moreover,instead of limiting the amplitude of control inputs,a smooth interpolation method is developed to create bumpless performance.Finally,the XV-15 tilt-rotor aircraft is chosen as a prototype to illustrate the effectiveness of this developed control method.展开更多
A novel identification algorithm is proposed to deal with the modelling issues of linear switched systems under the switching modes being unknown.The main contributions of this paper embody the following aspects:(1)fo...A novel identification algorithm is proposed to deal with the modelling issues of linear switched systems under the switching modes being unknown.The main contributions of this paper embody the following aspects:(1)for simplifying the identification problems,the label functions are proposed to replace the switching states of the modes;(2)The recursive least square algorithm is used to identify the system parameters,and the convergence performance of the proposed algorithm is studied.By using convergence analysis,the parameter estimation error can converge to zero point when the input signals satisfy persistent excited conditions and the total time of mode mismatch is limited.Finally,the effectiveness of the proposed method is verified by a simulation example.展开更多
This paper considers the problem of approximating the infinite-horizon value function of the discrete-time switched LQR problem.In particular,the authors propose a new value iteration method to generate a sequence of ...This paper considers the problem of approximating the infinite-horizon value function of the discrete-time switched LQR problem.In particular,the authors propose a new value iteration method to generate a sequence of monotonically decreasing functions that converges exponentially to the value function.This method facilitates us to use coarse approximations resulting from faster but less accurate algorithms for further value iteration,and thus,the proposed approach is capable of achieving a better approximation for a given computation time compared with the existing methods.Three numerical examples are presented in this paper to illustrate the effectiveness of the proposed method.展开更多
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.
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.
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.
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.
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.
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.
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 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.
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(61304058,61233002)IAPI Fundamental Research Funds(2013ZCX03-01)
文摘This paper focuses on the H_∞ model reference tracking control for a switched linear parameter-varying(LPV)model representing an aero-engine. The switched LPV aeroengine model is built based on a family of linearized models.Multiple parameter-dependent Lyapunov functions technique is used to design a tracking control law for the desirable H_∞ tracking performance. A control synthesis condition is formulated in terms of the solvability of a matrix optimization problem.Simulation result on the aero-engine model shows the feasibility and validity of the switching tracking control scheme.
文摘For linear switched system with both parameter uncertainties and time delay, a delay-dependent sufficient condition for the existence of a new robust H∞ feedback controller was formulated in nonlinear matrix inequalities solvable by an LMI-based iterative algorithm. Compared with the conventional state-feedback controller, the proposed controller can achieve better robust control performance since the delayed state is utilized as additional feedback information and the parameters of the proposed controllers are changed synchronously with the dynamical characteristic of the system. This design method was also extended to the case where only delayed state is available for the controller. The example of balancing an inverted pendulum on a cart demonstrates the effectiveness and applicability of the proposed design methods.
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 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 in part by the National Natural Science Foundation of China under Grant Nos.6177322561773236,61873331,61803225in part by the Taishan Scholar Project of Shandong Province under Grant No.TSQN20161033。
文摘The issues of event-triggered exponential L1 filtering are studied for a class of networked linear switched systems.An event-triggered mechanism is proposed to enhance resource utilization in transmission,and save the communication cost of systems as well.Then,the filtering error system is reconstructed as a switched delay system with bounded disturbance through the input delay system approach.By resorting to the Lyapunov-Krasovskii functional approach and the average dwell time(ADT)technique,some interesting results are derived to guarantee the exponential stability with a prescribed L1 disturbance rejection level.Further,an event-triggered exponential L1 filter is designed via solving a set of feasible linear matrix inequalities(LMIs).Finally,the efficiency of the proposed results is verified through a numerical example and a PWM-driven boost converter circuit system.
基金Project supported by the National Natural Science Foundation of China (Nos.62103186 and 62122038)the Natural Science Foundation of Jiangsu Province,China (Nos.BK20210285 and BK20211565)the China Postdoctoral Science Foundation (Nos.2021TQ0151 and 2021M691571)。
文摘This paper investigates the state-tracking control problem in conversion mode of a tilt-rotor aircraft with a switching modeling method and a smooth interpolation technique.Based on the nonlinear model of the conversion mode,a switched linear model is developed by using the Jacobian linearization method and designing the switching signal based on the mast angle.Furthermore,an ℋ_(∞) state-tracking control scheme is designed to deal with the conversion mode control issue.Moreover,instead of limiting the amplitude of control inputs,a smooth interpolation method is developed to create bumpless performance.Finally,the XV-15 tilt-rotor aircraft is chosen as a prototype to illustrate the effectiveness of this developed control method.
基金supported byNational Natural Science Foundation of China[grant number 61863034].
文摘A novel identification algorithm is proposed to deal with the modelling issues of linear switched systems under the switching modes being unknown.The main contributions of this paper embody the following aspects:(1)for simplifying the identification problems,the label functions are proposed to replace the switching states of the modes;(2)The recursive least square algorithm is used to identify the system parameters,and the convergence performance of the proposed algorithm is studied.By using convergence analysis,the parameter estimation error can converge to zero point when the input signals satisfy persistent excited conditions and the total time of mode mismatch is limited.Finally,the effectiveness of the proposed method is verified by a simulation example.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.62022055 and 61973215。
文摘This paper considers the problem of approximating the infinite-horizon value function of the discrete-time switched LQR problem.In particular,the authors propose a new value iteration method to generate a sequence of monotonically decreasing functions that converges exponentially to the value function.This method facilitates us to use coarse approximations resulting from faster but less accurate algorithms for further value iteration,and thus,the proposed approach is capable of achieving a better approximation for a given computation time compared with the existing methods.Three numerical examples are presented in this paper to illustrate the effectiveness of the proposed method.
