As a typical class of hybrid systems, positive switched systems with time-delays are of great significance both in theory development and engineering applications. Such systems have broad applications in power electronics, communication systems and biology systems, and so on. However, there are little results have been obtained on such problem, which motivated the authors’study. The main contents of this paper are summarized as follows:Based on the multiply co-positive type Lyapunov-Krasovskii functional method and average dwell time approach, the exponential stability criterion and L1performance for positive switched systems with delays are derived. Firstly, sufficient conditions of exponential stability are given, and based on the derived results, L1performance is further studied, which made the system not only satisfy exponential stability and also have L1performance.For delayed positive switched systems with both stable and unstable subsystems, this paper will study the problems of reliable control. Firstly, sufficient conditions of exponential stability criterion are given. Based on the obtained results, exponential L1performance is further investigated. Next, the desired reliable controller is derived to guarantee the exponential stability of the corresponding closed-loop system with L1-gain property.Considering the common phenomena of the switched times of controllers and subsystems are not matched in actual operation, which is called asynchronous switching. This paper will investigate the problems based on the average dwell time and mode-dependent average dwell time methods for delayed positive switched systems. And robust L1stability feedback controller are also designed in this part.Finally, this paper will concern the problems of L1finite-time control for a class of positive switched systems with time-varying delay. And the concepts of finite-time stability, finite-time boundedness and L1finite-time boundedness are first given. Then, sufficient conditions of finite-time boundedness are derived and a set of state feedback controllers are designed to guarantee the closed-loop system is L1finite-time bounded. |