Stability Analysis For Several Classes Of Discrete Switched Systems

Switched systems are composed of finite subsystems and a switching rule that su-pervises the switching between subsystems. Appropriate switching can improve the per-formance of the systems. In real life, switching phenomenon exists in many industries,such as the manufacturing systems, traffic control system and so on. Discrete switched systems, which is an important branch of the control system theory, have high research value in controlling engineering and control theory. In this paper, we study the stability of several classes of discrete switched systems. The main results of this dissertation can be summarized as follows:1?The finite-time control problem for a class of discrete singular switched systems with multiple delays is considered. By introducing a new variable, the discrete singular switched systems are transformed into nonsingular discrete switched systems. With the help of Lyapunov-Krasovskii function and mode-dependent average dwell time approach,we give sufficient conditions for the finite-time boundedness and l1 finite-time boundedness of such switched systems.2?The absolute exponential l1 stability for a class of nonlinear positive discrete switched systems is analyzed. In the case of allowing the Lyapunov-Krasovskii function of the subsystems increasing, based on the mode-dependent average dwell time method,sufficient, conditions which guarantee the stability of the absolute exponential l1 under the asynchronous switching, are derived.3?The input-to-state stability analysis for a class of nonlinear cascaded discrete switched systems is studied. Two cases are discussed: one is that all the subsystems are stable; and the other is that some subsystems are not stable. The sufficient conditions for input-to-state stability of the system are given respectively.