In the development of linear quadratic regulator(LQR) algorithms, the Riccati equation approach offers two important characteristics——it is recursive and readily meets the existence condition. However, these attribu...In the development of linear quadratic regulator(LQR) algorithms, the Riccati equation approach offers two important characteristics——it is recursive and readily meets the existence condition. However, these attributes are applicable only to transformed singular systems, and the efficiency of the regulator may be undermined if constraints are violated in nonsingular versions. To address this gap, we introduce a direct approach to the LQR problem for linear singular systems, avoiding the need for any transformations and eliminating the need for regularity assumptions. To achieve this goal, we begin by formulating a quadratic cost function to derive the LQR algorithm through a penalized and weighted regression framework and then connect it to a constrained minimization problem using the Bellman's criterion. Then, we employ a dynamic programming strategy in a backward approach within a finite horizon to develop an LQR algorithm for the original system. To accomplish this, we address the stability and convergence analysis under the reachability and observability assumptions of a hypothetical system constructed by the pencil of augmented matrices and connected using the Hamiltonian diagonalization technique.展开更多
This paper introduces a Kalman-type recursive state estimator for a class of discrete-time stochastic linear singular systems where the measurements are carried part by part periodically following a scheduling algorit...This paper introduces a Kalman-type recursive state estimator for a class of discrete-time stochastic linear singular systems where the measurements are carried part by part periodically following a scheduling algorithm.We consider that the system is in a network with limited allotted bandwidth,which refers to a situation where the total available bandwidth for data transmission through the network is limited.This limitation can occur for various reasons,such as network congestion,resource allocation policies,or bandwidth limitations imposed by network administrators.In such networks,the entire measurement vector cannot be transmitted to the estimator instantly.Thus,managing a network with a limited allotted bandwidth requires careful planning,monitoring,and implementing some scheduling strategies to optimize the use of measured data while estimating the system states.We show that a scheduling method,namely,round-robin protocol,is suitable for singular systems to deal with such a scenario.The upper bound of the prior error covariance is studied via a periodic Riccati equation(PRE).To retain the boundedness of prior error covariance,the stability of the PRE is examined by the observability properties of the round-robin-induced system.Finally,a simulation example is presented to show the effectiveness of the designed filtering scheme.展开更多
The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First...The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.展开更多
The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapuno...The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapunov function and Lyapunov stability theory. Based on which, a sufficient condition is presented such that the system is zero solution asymptotically stable and has H∞ norm constraint γ. Then, the static output feedback H∞ controller is designed to guarantee the resulting closed-loop system has the same performance. Finally, an example proves the effectiveness of the conclusion.展开更多
The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for...The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e....The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.展开更多
The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and n...The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.展开更多
This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the un...This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities （LMIs）. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.展开更多
This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality （LMI） approach. Based on a delay-d...This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality （LMI） approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed- loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.展开更多
The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is propo...The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.展开更多
The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new ...The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities （LMIs）. Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.展开更多
Based on input-output approach, the robust stability and stabilization problems for uncertain singular systems with time-varying delays are investigated. The parameter uncertainties are assumed to be norm-bounded and ...Based on input-output approach, the robust stability and stabilization problems for uncertain singular systems with time-varying delays are investigated. The parameter uncertainties are assumed to be norm-bounded and the time-varying delays include both discrete delay and distributed delay. By introducing a new input-output model, the time-delay system is embedded in a family of systems with a forward system without time delay and a dynamical feedback uncertainty. A sufficient and necessary condition, which guarantees the system regular, impulse-free and stable for all admissible uncertainties, is obtained. Based on the strict linear matrix inequality, the desired robust state feedback controller is also obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.展开更多
A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a suffic...A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a sufficient condition for the solvability of the H-infinity control problem for SISSs is given which generalizes the H-infinity control theory for singular systems to switched singular systems with impulsive effects. Then the sufficient condition of solvablity of the H-infinity control problem is presented in terms of linear matrix inequalities. Finally, the effectiveness of the developed aooroach for switched and imoulsive singular svstems is illustrated by a numerical example.展开更多
This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and th...This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and the integral multiples of a constant delay. Specially, if the constant delay is of unit length, the delay is an interval-like time-varying delay. The proposed admissibility condition is presented and expressed in terms of linear matrix inequality (LMI) by Lyapunov approach. Generally, the uncertainty of time-varying delay would lead to conservatism. In this paper, this critical issue is tackled by accurately estimating the time-varying delay. Consequently, the proposed admissibility condition is less conservative than the existing results, which is demonstrated by a numerical example.展开更多
The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By ...The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities（LMIs）.An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms（ignored in previous methods） when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.展开更多
This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based o...This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.展开更多
The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in app...The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities （LMIs）. Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.展开更多
Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional p...Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional primary constraints and the fractional constrained Hamilton equations are given.Then,the fractional Noether theorems of the two fractional singular systems are established,including the fractional Noether identities,the fractional Noether quasi-identities and the fractional conserved quantities.Finally,the results obtained are illustrated by two examples.展开更多
The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite ...The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.展开更多
In this paper, we define the ({A,E},B)-invariant subspace pair contained in Ker C for singular systems, rigorously justifying the name and demonstrating the existence of the supremal ({A,E},B)-invariant;subspace pair ...In this paper, we define the ({A,E},B)-invariant subspace pair contained in Ker C for singular systems, rigorously justifying the name and demonstrating the existence of the supremal ({A,E},B)-invariant;subspace pair contained in Ker C, we show how the supremal ({A,E},B)-invariant subspace pair contained in Ker C can be computed via some subspace recursions, We provide necessary and sufficient condition for the existence of a state feedback that achieves disturbance localization in a linear time-invariant singular system.展开更多
基金supported by the European Union’s Horizon Europe research and innovation programme (101120657)project ENFIELD (European Lighthouse to Manifest Trustworthy and Green AI), the Estonian Research Council (PRG658, PRG1463)the Estonian Centre of Excellence in Energy Efficiency, ENER (TK230) funded by the Estonian Ministry of Education and Research。
文摘In the development of linear quadratic regulator(LQR) algorithms, the Riccati equation approach offers two important characteristics——it is recursive and readily meets the existence condition. However, these attributes are applicable only to transformed singular systems, and the efficiency of the regulator may be undermined if constraints are violated in nonsingular versions. To address this gap, we introduce a direct approach to the LQR problem for linear singular systems, avoiding the need for any transformations and eliminating the need for regularity assumptions. To achieve this goal, we begin by formulating a quadratic cost function to derive the LQR algorithm through a penalized and weighted regression framework and then connect it to a constrained minimization problem using the Bellman's criterion. Then, we employ a dynamic programming strategy in a backward approach within a finite horizon to develop an LQR algorithm for the original system. To accomplish this, we address the stability and convergence analysis under the reachability and observability assumptions of a hypothetical system constructed by the pencil of augmented matrices and connected using the Hamiltonian diagonalization technique.
基金supported by the Science and Engineering Research Board,New Delhi(No.MTR/2019/000494).
文摘This paper introduces a Kalman-type recursive state estimator for a class of discrete-time stochastic linear singular systems where the measurements are carried part by part periodically following a scheduling algorithm.We consider that the system is in a network with limited allotted bandwidth,which refers to a situation where the total available bandwidth for data transmission through the network is limited.This limitation can occur for various reasons,such as network congestion,resource allocation policies,or bandwidth limitations imposed by network administrators.In such networks,the entire measurement vector cannot be transmitted to the estimator instantly.Thus,managing a network with a limited allotted bandwidth requires careful planning,monitoring,and implementing some scheduling strategies to optimize the use of measured data while estimating the system states.We show that a scheduling method,namely,round-robin protocol,is suitable for singular systems to deal with such a scenario.The upper bound of the prior error covariance is studied via a periodic Riccati equation(PRE).To retain the boundedness of prior error covariance,the stability of the PRE is examined by the observability properties of the round-robin-induced system.Finally,a simulation example is presented to show the effectiveness of the designed filtering scheme.
基金The National Natural Science Foundation of China(No.60835001)the Key Project of Ministry of Education of China (No.108060)
文摘The robust admissibility analysis of a class of uncertain discrete-time switched linear singular（SLS） systems for arbitrary switching laws is addressed. The parameter uncertainty is assumed to be norm-bounded. First, by using the switched Lyapunov function approach, some new sufficient conditions ensuring the nominal discrete-time SLS system to be regular, casual and asymptotically stable for arbitrary switching laws are derived in terms of linear matrix inequalities. Then, the robust admissibility condition for the uncertain discrete-time SLS systems is presented. The obtained results can be viewed as an extension of previous works on the switched Lyapunov function approach from the regular switched linear systems to the switched linear singular cases. Numerical examples show the reduced conservatism and effectiveness of the proposed conditions.
基金supported by the National Natural Science Foundation of China (60574011)
文摘The static output feedback H∞ control is explored for a class of nonlinear singular system with norm-bounded uncertainty. On certain suppose, the zero solution asymptotically stability is analyzed by means of Lyapunov function and Lyapunov stability theory. Based on which, a sufficient condition is presented such that the system is zero solution asymptotically stable and has H∞ norm constraint γ. Then, the static output feedback H∞ controller is designed to guarantee the resulting closed-loop system has the same performance. Finally, an example proves the effectiveness of the conclusion.
基金supported by Research Foundation of Education Bureau of Shannxi Province, PRC(No.2010JK400)
文摘The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
基金Postdoctoral Science Foundation of China (No. 20060400980)Postdoctoral Science Foundation of Shandong Province(No. 200603015)National Science Foundation of China (No. 10671112)
文摘The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.
基金supported by the National Natural Science Foundation of China (60564001)the Program for New Century Excellent Talentsin University (NCET-06-0756)
文摘The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.
文摘This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities （LMIs）. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.
基金the National Natural Science Foundation of China (No.60503027)
文摘This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality （LMI） approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed- loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.
基金supported by the National Natural Science Foundation of China(60774016).
文摘The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.
基金supported partly by the National Natural Science Foundation of China(6057400660835001)+1 种基金the Key Project of Chinese Ministry of Education(108060)the Jiangsu Planned Projects for Postdoctoral Research Funds(0802010c).
文摘The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities （LMIs）. Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.
基金Project supported by the Key Program of the National NaturalScience Foundation of China (No. 60434020)the National Natural Science Foundation of China (No. 60604003)
文摘Based on input-output approach, the robust stability and stabilization problems for uncertain singular systems with time-varying delays are investigated. The parameter uncertainties are assumed to be norm-bounded and the time-varying delays include both discrete delay and distributed delay. By introducing a new input-output model, the time-delay system is embedded in a family of systems with a forward system without time delay and a dynamical feedback uncertainty. A sufficient and necessary condition, which guarantees the system regular, impulse-free and stable for all admissible uncertainties, is obtained. Based on the strict linear matrix inequality, the desired robust state feedback controller is also obtained. Finally, a numerical example is provided to demonstrate the application of the proposed method.
基金the National Natural Science Foundation of China (No.60574013)the Science and Technology Foundation of theEducation Department of Liaoning Province (No.20060823)
文摘A new model of dynamical systems is proposed which consists of singular systems with impulsive effects, i.e., switched and impulsive singular systems （SISS）. By using the switched Lyapunov functions method, a sufficient condition for the solvability of the H-infinity control problem for SISSs is given which generalizes the H-infinity control theory for singular systems to switched singular systems with impulsive effects. Then the sufficient condition of solvablity of the H-infinity control problem is presented in terms of linear matrix inequalities. Finally, the effectiveness of the developed aooroach for switched and imoulsive singular svstems is illustrated by a numerical example.
基金supported by National Natural Science Foundation of China (Nos.61035005,61175041,60904009)Program for Liaoning Excellent Talents in University (No. LJQ2011118)Natural Science Foundation of Liaoning Province (No. 201202201)
文摘This paper gives a novel delay-dependent admissibility condition of discrete-time singular systems with time-varying delays. For convenience, the time-varying delay is assumed to be the sum of delay lower bound and the integral multiples of a constant delay. Specially, if the constant delay is of unit length, the delay is an interval-like time-varying delay. The proposed admissibility condition is presented and expressed in terms of linear matrix inequality (LMI) by Lyapunov approach. Generally, the uncertainty of time-varying delay would lead to conservatism. In this paper, this critical issue is tackled by accurately estimating the time-varying delay. Consequently, the proposed admissibility condition is less conservative than the existing results, which is demonstrated by a numerical example.
基金supported by the National Natural Science Foundation of China(6090402060835001)the Jiangsu Planned Projects for Postdoctoral Research Funds(0802010C)
文摘The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities（LMIs）.An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms（ignored in previous methods） when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.
基金This work was supported by the National Natural Science Foundation of China (No. 6022130, 60334040, 60428304).
文摘This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.
基金supported by National Natural Science Foundation of China(No.11071193)Research Foundation of Education Bureau of Shan xi Province(No.11JK0509)Research Foundation of Baoji University of Arts and Sciences(No.ZK11044)
文摘The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities （LMIs）. Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.
基金Supported by the National Natural Science Foundation of China(12172241,12002228,12272248,11972241)Qing Lan Project of Colleges and Universities in Jiangsu Province
文摘Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional primary constraints and the fractional constrained Hamilton equations are given.Then,the fractional Noether theorems of the two fractional singular systems are established,including the fractional Noether identities,the fractional Noether quasi-identities and the fractional conserved quantities.Finally,the results obtained are illustrated by two examples.
基金Project (Nos. 60434020 and 60604003) supported by the NationalNatural Science Foundation of China
文摘The design problem of delay-dependent robust control for uncertain discrete singular systems with time-varying delay is addressed in this paper. The uncertainty is assumed to be norm-bounded. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent robust stability condition is derived and expressed in terms of linear matrix inequalities (LMIs). A suitable robust state feedback control law is presented, which guarantees that the resultant closed-loop system is regular, causal and stable for all admissible uncertainties. Numerical examples are given to demonstrate the applicability of the proposed method.
文摘In this paper, we define the ({A,E},B)-invariant subspace pair contained in Ker C for singular systems, rigorously justifying the name and demonstrating the existence of the supremal ({A,E},B)-invariant;subspace pair contained in Ker C, we show how the supremal ({A,E},B)-invariant subspace pair contained in Ker C can be computed via some subspace recursions, We provide necessary and sufficient condition for the existence of a state feedback that achieves disturbance localization in a linear time-invariant singular system.
