Robust H_∞ Control For Singular Switched LPV Systems With Time-delay

The switched systems are a class of typical hybrid systems.Different with other systems,the structure of switched systems is composed of multiple subsystems,the switched modes between subsystems will have certain influence on the stability of the systems.Therefore,the design of switched rules is significant.This paper investigates the stability of the switched systems by utilizing the average dwell time and exponential stability method to study.In addition,compared with normal systems,the model of singular systems,which is more general,can be widely used to describe systems.Linear parameter varying(LPV)system is a kind of timevarying system,where the state space matrices are deterministic functions of the time-varying parameters which can be measured in real time.This paper studies exponential stability analysis and H∞ controller design of the singular time-delay switched LPV systems.The main research contents are as follows:1.The problem of H∞ control is investigated for switched LPV systems with time-delay.Firstly,the state feedback controller design and exponential stability of the switched LPV systems with constant time-delay systems are studied by means of average dwell time.By using linear matrix inequality,the sufficient conditions for the systems,which are exponential stability and satisfy the H∞ performance,are proposed.Moreover,controller gain matrix is obtained.Then,the exponential stability and the H∞ performance level of the time-delay uncertain switched LPV system are studied and controller gain matrix is obtained.Finally,the simulation results are provided to demonstrate the validity and applicability of the proposed control scheme.2.The problem of H∞ control is investigated for switched LPV systems with time-varying delay.Firstly,the exponential stability of the switched LPV systems with time-varying delay are studied by means of parameter dependent Lyapunov-Krasovskv functions and integral inequalities.The H∞ performance level of the switched LPV systems with time-varying delay are studied and controller gain matrix is obtained.Secondly,there is coupling between coefficient matrix and parameter dependent Lyapunov-Krasovskvii function.The new criterion is obtained by means of projection lemma.The gain matrix of the controller can be obtained by the method of approximate basis function,which transforms the linear matrix inequality of infinite dimension into finite dimension.Finally,the simulation results are provided to demonstrate the validity and applicability of the proposed control scheme.3.The problems of H∞ control and exponential stability are investigated for singular switched LPV systems with time-varying delay.Firstly,the nominal systems are proved to be regular and impulse-free.The stability of the nominal systems are analyzed by parameter dependent Lyapunov-Krasovskv functional and free weight matrix.Secondly,the exponential stability and the H∞ performance level of the closed loop systems are studied.The gain matrix of the controller is obtained by means of congruent transformation.Finally,the simulation results are provided to demonstrate the validity and applicability of the proposed control scheme.