Stochastic Finite-time Control For Positive Markov Jump Linear Systems With Time-delay

This thesis is concerned with stochastic finite-time control problem of positive Markov jump linear systems?MJLSs?with time-delay in both continuous-time and discrete-time contexts.For a class of discrete-time positive MJLSs with constant time-delay and a class of continuous-time positive MJLSs with interval time-varying delay and partly known transition rates,the conditions of stochas-tic finite-time boundedness and finite-time l₁/L₁-gain performance are presented based on linear programming?LP?.Then the design methods of the stochastic finite-time l₁/L₁ state feedback controller for these two classes of systems are given.The main body contains three chapters.Chapter 1 introduces the research background of this thesis.The research progress of positive MJLSs,as well as the research history and current status of finite-time control theory,are presented systematically.Accordingly,the research gap of stochastic finite-time control for positive MJLSs is pointed out,which leads to the main work of this thesis.Finally,the used notations are listed.In Chapter 2,the stochastic finite-time control problem for a class of discrete-time positive MJLSs with constant time-delay is investigated.By using the indi-cator function based on Markov sequence,the stochastic finite-time control prob-lem for this type of systems is equivalently transformed into the finite-time control problem for the according deterministic time-delay positive linear systems.By analyzing the finite-time boundedness and finite-time l₁-gain performance for the deterministic time-delay positive linear systems,the delay-dependent criteria of stochastic finite-time stability,stochastic finite-time bounedeness and finite-time l₁-gain performance for the discrete-time positive MJLSs with constant time-delay are given.Moreover,the design met,hod of the stochastic finite-time l₁ state feed-back controller is given by solving an LP problem.The effectiveness of the design method is illustrated by a detailed numerical example.In Chapter 3,the stochastic finite-time control problem for a class of continuous-time positive MJLSs with interval time-varying delay and partly known transi-tion rates is studied.By constructing an appropriate linear co-positive stochastic Lyapunov-Krasovskii functional which makes full use of the upper bound and lower bound of the interval time-varying delay,some delay-dependent conditions of the stochastic finite-time boundedness and finite-time L₁-gain performance are established for the first time,and a stochastic finite-time L₁ state feedback con-troller design method is presented by resolving an LP problem.The simulation results of the numerical example at the end of this chapter show the effectiveness of the derived criterion.