Performance Analysis And Control Of Periodic Piecewise Linear System Under Communication Delay

Periodic characteristics broadly exist in engineering applications.Since the 19th century,the theory and the control problems of periodic systems have been studied by many scholars.In recent years,the periodic piecewise linear system,as a special kind of system with hybrid and periodic characteristics,is considered to be the most effective approximation method for periodic time-varying systems.Periodic piecewise linear system composed of a number of subsystems,in which the dwell time and switching sequence of each time-invariant/time-varying subsystem are fixed.In the network communication,delays and packet loss will inevitably occur.To solve this problem,many results have been achieved by scholars.However,in the networked periodic piecewise linear systems,the network transmission delay in communication channels results in the control input delay and the asynchronous switching between systems and controllers,that is,the asynchronous control problem.However,few results have been reported on the asynchronous problem of networked periodic piecewise linear systems.Therefore,the study of the asynchronous control of the networked periodic piecewise linear systems are important both in theory development and applications.In this thesis,the stability,H_?performance analysis,finite-time stability,and the robust non-fragile controller design are studied for continuous-time periodic piecewise linear time-invariant systems.The main results are given as follows:(1)The stability and H_? performance of networked periodic piecewise linear time-invariant system are studied.Based on the Lyapunov-Krasovskii functional with a periodic time-varying matrix functions,the time-delay exponential stability conditions are obtained.Moreover,the H_?performance of the system is studied,and the controller gain of the system is obtained by an iterative algorithm.(2)The design of non-fragile controller is studied for networked periodic piecewise linear system.Based on the Lyapunov function with periodic time-varying matrix functions and free weight matrix method,two types of uncertain controller gain disturbances with periodic time-varying matrix parameters are considered.Based on the iterative algorithm,a periodic time-varying non-fragile controller is designed.(3)For the continuous time networked piecewise linear system,the problem of finite-time stability analysis is studied.Based on the Lyapunov function with periodic time-varying matrix functions,sufficient conditions for finite-time stability are obtained.