Research On Asynchronous Tracking Control And Finite Time Stability Of Switched Systems

As a class of important and special hybrid systems in the control field,the switched systems have important theoretical value and extensive practical background.In recent years,many significant progresses have been made in the research of switched systems,but there are still many problems not to be solved.Especially,little attention has been paid to the tracking control problem for switched systems under asynchronous switching.Based on the mode-dependent average dwell time method,this paper addresses the asynchronous H_?output tracking control problem for a class of continuous switched systems,and the idea of switching is used to study the finite-time model reference state tracking control problem for a class of continuous systems.The main contribution can be summarized as follows:1.The issue of H_?output tracking control is studied for a class of switched systems with time-varying delay via mode-dependent average dwell time method.By constructing the multiple Lyapunov functions,the conditions satisfied by the mode-dependent average dwell time are developed to ensure that the considered systems are exponentially stabilizable with H_?output tracking performance.At the same time,the switching controller combining state feedback and tracking error integral is also designed.The simulation example shows that the obtained results have better H_?tracking performance.2.By considering phenomenon that the switching between controllers lags behind that between system modes,an asynchronous switching controller combining state feedback and tracking error integral is proposed.Based on the mode-dependent average dwell time method,the solvability conditions for the H_?output tracking control for switched time-delay systems under asynchronous swithcing are derived in the form of linear matrix inequalities.Numerical simulation results show that the proposed design scheme of switching law is less conservative and has a wider range of applications.3.Based on the idea of switching,the state tracking problem of finite-time model reference control for linear systems is studied.First,according to the error between the system state and the reference model state,the controlled system is divided into matched and unmatched cases.The switching law of the controller is designed via the comparison of the state error and the threshold,and then the linear systems are converted into linear switched systems.The average dwell time method and finite time stability theory are used to obtain the conditions that the average dwell time satisfies such that the error systems are finite-time boundedness,and the design scheme of switching controller is also derived simultaneously.Simulation example is provided to illustrate the effectiveness of the proposed theoretical result.