Robust admissibility analysis of uncertain switched singular systems:a switched Lyapunov function approach

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.

Output Feedback Controller Design for Discrete-time Switched Singular Systems

This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The objective is to design a suitable robust SOF controller guaranteeing the regularity,causality and asymptotic stability of the resulting closed-loop system under arbitrary switching laws. Based on the basic matrix inequality sufficient condition for checking the admissibility of switched singular systems,together with some matrix inequality convexifying techniques,the SOF controller synthesis is developed for the underlying systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities( LMIs). A simulation example is given to show the effectiveness of the proposed method.

Input-to-State Stability for Impulsive Switched Singular Systems with Mismatched Disturbances

This work investigates the input-to-state stability(ISS)problem for impulsive switched singular systems(ISSSs)with mismatched disturbances.In this paper,‘disturbance’is a general concept that includes model uncertainty,unknown system dynamic,external disturbance,etc.The modified uncertainty and disturbance estimator(UDE)-based control method is presented for singular systems and ISSSs,a virtual control is introduced to offset the effects of mismatched disturbances.On the basis of a discontinuous multiple Lyapunov functional and admissible edge-dependent average dwell time(AED-ADT)method,several sufficient conditions in terms of linear matrix inequalities(LMIs)are obtained to ensure that the closed-loop systems are regular,impulse-free and ISS.Finally,two examples are given to demonstrate the effectiveness of the proposed results.

Admissibility analysis and control synthesis for switched linear singular systems

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.

H-infinity control for switched and impulsive singular systems

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.