The Event-triggered Control Of Two Classes Of Discrete-time Systems

Since event-triggered control has the advantage of saving the network resource and reducing the energy consumption with respect to the traditional time-triggered control, the research on event-triggered control gets more and more attention. Recently, the study on event-triggered control mainly focus on the stability of networked systems, regardless of the co-design of the event triggered condition and the controller. On the other hand, most of the results are about the certain systems. The studies about the robust event-triggered control of the uncertain systems haven’t been seen. So this paper will study the robust event-triggered control of uncertain linear discrete-time systems. At the same time, to the best of our knowledge, the study on switched systems based on the event-triggered control haven’t been seen. So this paper studies the event-triggered control problem about two classes systems one is discrete-time switched system, and the other is uncertain discrete-time linear system.Firstly, we study the ISS problem of discrete-time switched system based on event-triggered control. The feedback control law and event triggered condition of discrete-time switched linear system are co-designed which force the system is ISS.. Applying the common ISS-Lyapunov function method, a sufficient condition of the co-design of the feedback control gain and the event trigger condition are presented, under which two kinds different of event triggered condition. In addition, the next instant of event trigger is also studied, and present the formulation that can solve the next time instance to ensure the trigger interval between two events is greater than 1, which will avoid Zeno behavior.Secondly, we study the uncertain discrete-time system based on event-triggered control. We solve the problem of the co-design of feedback control gain and the event triggered condition which makes the system is ISS. Applying the ISS-Lyapunov function method,we give the sufficient condition of solving the problem. Besides, the robust control problem of the uncertain discrete-time system based on the event-triggered control is studied. We give the method on co-design of the H∞ controller and the event triggered condition that makes the system is asymptotically stable.Finally, the main results of this paper are summarized and the shortages of the study are pointed out. Moreover, some problems which will be studied in the future deserve further study are pointed out.