Design On Average Dwell Time Controller Of Switched System

The complicated control objects make the control performance more and more demanding.At the same time,the system operation mechanism is restricted by many factors,many practical control problems can be better solved by the theory of switched systems.Consequently,the analysis and comprehensive research on switched systems have become a hot issue in the academic and engineering research fields.The dynamic behavior of a switched systems depend not only on each subsystem,but also on the switching rules.ADT switching rules are demonstrated to be an effective techniqur to analyze switched systems stability and design controllers.After decades of research,the theory and application of switched systems have achieved fruitful results.However,there are still many problems to be further explored in the design of switched control systems.First,in the multiple Lyapunov functions-based controller design of switched systems,the jump boundary conditions of two adjacent Lyapunov functions are complex numerical calculation,a conservative solution of sufficient condition are achieved.Second,the design of weighted L₂ gain performance switching controller for switching systems have not been satisfactory.Finally,the design of the reduced-order controller for switched systems are also a key scientific problem.In view of the above three problems,this paper focuses on the average dwell time switching rule-based design techniques of switched controller.The specific research content mainly includes the following aspects.(1)In order to achieve the weighted L₂-gain performance of the discrete-time switched systems,the ADT-based design method of full-order output feedback switched controllers are proposed.The switched system performs reset rules at each switching instant,utilizing the linearization method of variable elimination method and variable substitution method,the sufficient conditions for the weighted L₂-gain performance are presented for discrete time switched systems.Then a dynamic output feedback control method for discrete time switching is designed.(2)In order to achieve the weighted L₂-gain performance of the continuous time switching LPV system.The ADT-based design method of output feedback switched controllers are proposed.The boundary condition that constrains the jump of two adjacent Lyapunov functions are often nonconvex.In this paper,a monitor that executes reset rules are introduced,a dynamic output feedback control method of continuous time switching is designed,for satisfying the sufficient condition ofweightedL₂-gain performance synthesis.Moreover,by matrix elementary transformation and Schur complement lemma,the boundary condition is transformed into linear matrix inequalities(LMIs),which make the switched system satisfy the weighted L₂-gain performance.(3)The weighted L₂-gain performance reduced-order controller for continuous time switching LPV systems are proposed.Generally,the order of the switched controllers are the same as that of the control system,and full-order controllers have high cost.In this paper,a reduced-order output feedback control method are proposed and compared with the traditional non-reset rule reduced-order one.(4)The parameterization design method of the weighted L₂-gain performance switching controller for the continuous time switching system.The ADT switching rules and multi Lyapunov functions are introduced to design a set of dynamic switching output feedback controller,Two forms of the solution methods,Riccati inequality ans LMTs are proposed to ensure that the closed-loop switching system satisfies the weighted L₂-gain performace,the controller parameterization form of the switching systems are given.