Stability For Discrete Positive Switched Systems With Mixed Time-varying Delays

Control theory possesses extensive application in social life and engineering field. In recent years, the switched control technique has attaracted great concern by relevant scholars. Switching systems are a class of important hybrid systems. Numerous results about stability for switching systems have been achieved. In recent years, some progress has been made on the stability of the positive switched systems, whose states can be only positive values. Some results concerning exponential stability, finite-time stability and stability under asynchronous switching were obtained. However, the relevant results for discrete-time positive switched systems is still limited. In this dissertation, we will discuss the exponential stability and finite-time control problem for a class of discrete-time positive switched system with mixed time-varying delays by constructing suitable co-positive Lyapunov-Krasovskii functions and making full use of the average dwell time and mode-dependent average time methods. The main contents are summarized as follows.First of all, by constructing a suitable co-positive type Lyapunov-Krasovskii functional, an exponential stability under asynchronous switching for a class of discrete-time positive switched system with mixed time-varying delays is derived by means of the average dwell time approach.Second, the finite-time control problem under asynchronous switching is discussed for a class of discrete-time impulsive positive switched system with mixed time-varying delays. Some sufficient conditions which guarantee the finite time stability and finite-time boundness are derived based on the mode-dependent average dwell time method by choosing a Lyapunov-Krasovskii functional.