Stochastic Finite-time Control And Filtering For Positive Markov Jump Linear Systems

The finite-time boundedness of one system means that the state of the system does not exceed a certain threshold during a fixed time interval when bounded initial condition and exogenous disturbance are given.This thesis is concerned with stochastic finite-time control and filtering for positive Markov jump linear systems.The problems of stochastic finite-time boundedness anal-ysis,controller design,performance analysis and positive filtering design for positive Markov jump linear systems have been discussed in both continuous-time and discrete-time contexts.Chapter 1 introduces the research background.Firstly,this chapter re-views the research background and existing results of positive Markov jump linear systems and finite-time control.Next,the problems of positive Markov jump linear systems in the filed of stochastic finite-time control and filtering have been proposed,also the main work of this thesis is given.Finally,the notations used in this thesis are listed.Chapter 2 discusses the problems of stochastic finite-time control and filtering for discrete-time positive Markov jump linear systems.The first sec-tion extends the definition of finite-time boundedness to discrete-time posi-tive Markov jump linear systems and by introducing the indicator function,the problem of stochastic finite-time boundedness analysis for positive Markov jump linear systems is transformed into the problem of finite-time boundedness analysis for the corresponding augmented system,then the sufficient condition of stochastic finite-time boundedness for positive Markov jump linear systems in the form of linear programming is conducted,and finite-time controller is designed further.In the second section,by analyzing the finite-time l1-gain performance of the augmented system,the sufficient condition of finite-time l1-gain performance for positive Markov jump linear systems has been proposed,also by solving a standard linear programming problem,the design method of finite-time positive l1-gain filtering has been obtained.Chapter 3 discusses the problems of stochastic finite-time control and fil-tering for continuous-time positive Markov jump linear systems.By setting the equivalence between the stochastic finite-time boundedness and L1-gain performance of continuous-time positive Markov jump linear systems and the finite-time boundedness and L1-gain performance of augmented deterministic continuous-time positive linear systems,the conditions of stochastic finite-time boundedness and finite-time L1-gain performance for positive Markov jump lin-ear systems has been obtained.Then the finite-time controller and finite-time positive L1-gain filter have been designed.