Control And Filtering Of Continuous-time Rectangular Descriptor Markov Jump Systems

In many practical systems,the number of system equations are generally different from the number of system variables,thus the rectangular descriptor Markov jump systems are more general than square descriptor Markov jump systems,which are widely used in circuit system,robot system,biological system,etc.Based on the rectangular descriptor Markov jump systems as the research framework,this dissertation mainly researches the indefinite linear quadratic(ILQ)optimal control for continuous-time rectangular descriptor Markov jump systems,robust H∞ dynamic output feedback control for nonlinear time-varying delay rectangular descriptor Markov jump systems,finite-time H∞ dynamic output feedback control for one-sided Lipschitz nonlinear rectangular descriptor Markov jump systems and resilient finite-time H∞ filtering for T-S fuzzy rectangular descriptor Markov jump systems.The dissertation mainly includes the following six chapters:In Chapter 1,the research background and current status of rectangular descriptor Markov jump systems,time delay systems,T-S fuzzy systems,linear quadratic(LQ)optimal control,dynamic output feedback control,and filter design are introduced.Then the basic lemmas used in this dissertation are given,and the work and innovations of this dissertation are summarized.In Chapter 2,the ILQ optimal control problem for continuous-time linear rectangular descriptor Markov jump systems is considered.Firstly,by using elementary linear algebra method,the ILQ problem for rectangular descriptor Markov jump systems can be equivalently transformed into standard LQ problem for Markov jump systems under some rank conditions and inequality conditions.Then based on the LQ theory of Markov jump systems,the solvable sufficient condition of the ILQ problem for rectangular descriptor Markov jump systems and the nonnegative optimal cost value are obtained,further,the differential subsystem of the resulting optimal closed-loop system can be ensured to have a unique solution.Finally,two numerical examples and a RC circuit example are provided to illustrate the effectiveness of the methods proposed in this chapter.In Chapter 3,the robust H∞ dynamic output feedback control for a class of nonlinear time-varying delay rectangular descriptor Markov jump systems is researched.Firstly,by using the method of dynamic compensation,the rectangular DOF controller is designed to make the closed-loop system as square descriptor Markov jump systems.Then by utilizing a mode-dependent and delay-dependent Lyapunov-Krasovskii(L-K)functional and implicit function theorem,sufficient conditions are given to guarantee that the augmented closed-loop systems are robust stochastically admissible with an H∞ performance and have unique solution.Further,based on certain matrix decoupling techniques,a new strict linear matrix inequality(LMI)sufficient condition for the existence of a rectangular dynamic output feedback control controller is obtained,and the controller is given.Finally,numerical examples are presented to verify the effectiveness and superiority of the results.In Chapter 4,the finite-time H∞ dynamic output feedback control for a class of one-sided Lipschitz nonlinear rectangular descriptor Markov jump systems is discussed.Firstly,the sufficient conditions are given to guarantee that the closed-loop systems are singular stochastic H∞ finite-time bounded and have a unique solution by adopting a mode-dependent Lyapunov functional and implicit function theorem.Then a strict LMI sufficient condition for the existence of a rectangular dynamic output feedback controller is given based the on certain matrix decoupling techniques,and the controller is obtained.Finally,three numerical examples are presented to verify the feasibility and validity of the results.In Chapter 5,the resilient finite-time H∞ filtering for T-S fuzzy rectangular descriptor Markov jump systems is investigated.Firstly,by utilizing a mode-dependent Lyapunov functional and introducing the free matrices method,sufficient conditions are given to guarantee that the filtering error systems are singular stochastic H∞ finite-time bounded.Then based on matrix decoupling techniques,the LMI design method of resilient filter is given.Finally,three examples are given to verify the validity and practicability of the results.In Chapter 6,the research work of this dissertation is summarized,and the future research work is prospected.