The Study On Event-Triggered Control Problems For A Class Of Switched Linear Systems

Switched systems are a class of hybrid systems with certain special properties.In recent years,many scholars in the field of control have conducted a lot of research on switched systems and obtained many results on the comprehensive problems of switched systems,such as stability,controllability,observability and stabilization problems.On the other hand,with the development of network control,event-triggered control has attracted widespread attention as a practical and effective control method,and it has been applied to a large number of industrial control systems.Compared with the traditional time-triggered control method,the event-triggered control method can effectively reduce the amount of information exchange in the controller,measuring transmitter and actuator in the industrial control system,and reduce the possibility of information delay or information loss in network transmission,and improve the operational efficiency of the process control unit.It is worth noting that time delay is a ubiquitous phenomenon both in the operation of the control system and in the transmission of the network system.The phenomenon of time delay is often an important factor affecting the performance of the system.During the execution of the system,the generation of large time delay sometimes destroys the original excellent performance of the system.Therefore,time delay is often one of the problems that cannot be ignored in the analysis and design of control systems.In addition,H?control,as a design method with good robustness,can be designed directly in the state space,with the advantages of computational accuracy and optimization.Based on the above related research issues,this paper mainly studies the event-triggered asynchronous feedback control problem of a class of switched linear systems.This paper constructs an event-triggered mechanism based on the characteristics of switched linear systems,designs a feedback controller that is constrained by the triggering mechanism to achieve the stability of the closed-loop system,and obtains sufficient conditions to ensure the index stability of the controlled system.The main research contents of this paper are as follows:(1)Combining the average dwell time switching method with event-triggered feedback control,the event-triggered control problem for a class of switched linear systems with time-delay is studied.The event-triggered control here refers to adding a sampling link in the loop in which the controlled system performs feedback.The sampling mechanism is activated only when the error state exceeds the designed dynamic threshold,samples the current system state,transmits the sampling information and gives feedback control to the controller.In this paper,the sufficient condition for the exponential stability of the closed-loop system under the event-triggered method are obtained.In addition,based on the designed triggering condition,it can ensure that there is a positive lower bound every two triggering time intervals,thus avoiding the occurrence of Zeno phenomenon.(2)The event-triggered feedback control problem for a class of continuous time switched linear systems is studied.By sampling the same event-triggered control method,a piecewise quadratic Lyapunov function is constructed,and the average dwell time switching method is used to obtain sufficient discriminant conditions for the closed-loop switched linear system to meet the performance index.Finally,the feasibility and effectiveness of the proposed method are verified by a numerical simulation.