Admissibility Analysis And Feedback Control Of Singular Linear Parameter-varying Systems

In this paper,the related problems of singular linear parameter-varying(LPV)systems are studied.These problems are mainly in three aspects,namely,admissibility analysis,state-feedback stabilization and extended dissipativity control.In addition,the problems of gain-scheduling control for singular LPV systems with uncertain parameters are also studied.Firstly,the constant time delay is introduced into the singular LPV system's model.By constructing the delay-dependent and parameter-dependent Lyapunov-Krasovskii functional,the admissibility criterion of the singular delay LPV systems is given in the form of matrix inequalities.For systems that do not meet the admissibility,a parameter-dependent state-feedback controller is designed to make the closed-loop systems meet the admissibility.Based on this,the gain matrix of the state-feedback controller is solved.Second,the disturbance is further introduced in singular time-delay LPV systems.An extended dissipativity covering a variety of common performance metrics in control systems is proposed.Then the design method of the gain-scheduling state-feedback controller is given in the form of matrix inequality.Under the action of the controller,the closed-loop systems will satisfy the admissibility without disturbance and the extended dissipativity with disturbance.Based on this,the gain matrix of the state-feedback controller is solved.Thirdly,for the status that the scheduling parameters of the state-feedback controller is inconsistent with the scheduling parameters in the singular LPV systems,a state-feedback controller whose scheduling parameters are dependent on Markovian stochastic processes is constructed.Under the action of the state feedback controller,the closed-loop systems become singular LPV systems of Markovian jumping.For the closed-loop system,the matrix inequality condition that satisfies the admissibility is given.Based on this,the gain matrix of the state feedback controller is solved.For the matrix inequality conditions given in each chapter,they are transformed into strict and finite linear matrix inequalities(LMI),which are easy to solve by using LMI toolbox of MATLAB.At the end of each chapter,some numerical examples are given.Combined with the methods and conclusions presented in the corresponding chapters,simulations are performed.The simulation results of these examples show the correctness and validity of the theorems.