Study On H-infinite Control And Filtering For Switched Singular Systems With Time Varying Delay Under Asynchronous Switching

As a class of special hybrid systems, switched singular system can describe more complex systems. Compared with the normal ones, the structure of switched singular systems is complicated. The existence of regularity, impulse-free(causally) and the compatibility of initial state at switching time makes the problem of controller designing and stability analysis become more difficulty. Moreover a large number of the existing results are based on the switched normal systems. Therefore, the study of switched singular system is very important theoretical value and practical application significance. Based on the Lyapunov function and average dwell time technology, finite-time stability analysis for switched singular is discussed. And then the issue of asynchronous H-infinite control and H-infinite filtering for switched singular systems with time-varying delays are presented. The main study contents are as follow:1) Finite-time stability(FTS) of switched linear singular systems is studied. At first, the definition of finite-time stability is extended to switched linear singular systems. Then, based on the description of the state jump by a consistency projector at the switching instant, we obtain a sufficient condition for FTS of switched linear singular systems utilizing a piecewise Lyapunov function and state dependent switching law which selects the activated mode with the minimum Lyapunov function along the trajectories of the states. Moreover a time dependent switching law is given such that the switched singular system is finite time stability and FTS for systems with both stable subsystems and unstable subsystems is concerned. Finally, the condition of H_∞finite time bounded for switched singular systems is proposed. Examples are presented to verify the effectiveness of the proposed menthods.2) The problem of H-finite control for switched singular system with time-varying delays under asynchronous control is discussed. Firstly, we transform the time-varying delay system into an input-output system. Based on the Lyapunov function and average dwell time technology, the stability condition of the switched singular systems with time-varying delays under asynchronous is proposed by using input-output methods. Also the regularity, impulse-free and H-infinite performance is guaranteed. At last the controllers can be obtained by solving a set of LMIs. Examples are provided to verify the efficiency of the proposed method.3) The issue of H-infinite filtering for discrete-time switched singular systems with time-varying delays under asynchronous control is concerned. Firstly, the state space model of the filtering error system is transformed into a new description. These two forms have the equivalent stability. And then, utilizing the multiple Lyapunov function and average dwell time technique a sufficient condition is derived so that the novel filtering error system is regular, causal and exponentially stable with a prescribed H-infinite performance bound. The decay rate of the states and the *g-disturbance attenuation level are all related to the mismatched time. Based on the condition, filter parameters can be obtained by solving a set of linear matrix inequalities. Finally, the effectiveness of the develop results are illustrated by an numerical example.