Research On Robust Control And Filter For Markov Jump Systems With Partly Unknown Transition Probabilities

As a special class of hybrid systems,Markov jump systems can model plants subject to sudden environment disturbances,changes in subsystems interconnec-tions,component failures,and so on.Due to their extensive application in the fields of control theory,circuits,economy,manufacturing,and so on,many fruitful results about stability,stabilization,act,uat,or saturation,finite-time control,and filtering have been reported.However,it is noticeable that most of the results about Markov jump systems have been obtained under the assumption of completely accessible knowledge of the transition probabilities.In practical physical systems,owing to the limitations of various measurement conditions,the transition probabilities are always partly unknown(or partly known).The dynamical behaviors of Markov jump systems are affected by the interaction among the continuous dynamic,the discrete dynamic,and the partly unknown transition probabilities,therefore,are very complicated.Many problems of analysis and syntheses need to be studied.This dissertation concerns the problems of robust control and filter for Markov jump systems with partly unknown transition probabilities.The main contributions are listed as follows.Chapter 2 concerns the issues of robust control and anti-windup design for stochastic Markov jump systems and stochastic time-delayed Markov jump systems with actuator saturation and partly unknown transition probabilities.By using the Lyapunov-Krasovskii functional,the free-connection weighting matrices,and the assumption of given output feedback controllers,sufficient conditions for stochastic stability and robustly stochastic stability of the closed-loop systems are proposed.The problems of deriving anti-windup compensation gain matrices and expanding the domain of attraction can be converted into a convex optimization problem with constraints of a set of linear matrix inequalities.Chapter 3 studies the problems of finite-time H? control for nonlinear stochas-tic Markov jump systems and improved stochastic Markov jump systems with time-varying delay and partly unknown transition probabilities.Firstly,by implying the Lyapunov-Krasovskii functional and the free-connection weighting matrices,suffi-cient conditions for finite-time boundedness and finite-time H? boundedness of the closed-loop systems are given.Then,based on the obtained results,solution of the finite-time H? state feedback controller is proposed.Finally,the problem of de-riving finite-time H? state feedback controller can be converted into a feasibility problem with constraints of a set of linear matrix inequalities.When studying finite-time H? control for improved stochastic Markov jump systems with time-varying delay,finite-time stability is redefined and new Lyapunov-Krasovskii functional is constructed,which can release the restrictive condition on time-varying delay whose derivative must be less than 1 and reduce some conservativeness.Chapter 4 concerns the issues of L1 control for positive Markov jump systems and singular positive Markov jump systems with partly unknown transition prob-abilities.Compared with previous quadratic Lyapunov-Krasovskii functional,by implying the linear Lyapunov-Krasovskii functional and the free-connection weight-ing vectors,sufficient conditions for stochastic stability and L1 boundedness of the systems are proposed.For given L1-gain parameter,the problem of deriving state feedback controller gain matrices can be converted into the feasibility problem in the form of linear programming.When studying L1 control for singular positive Markov jump systems,singular positive Markov jump systems can be changed into equivalent nonsingular positive Markov jump systems,which can be convenient for the solution of related problems.Chapter 5 deals with the problems of L1 control and finite-time L1 control for positive Markov jump systems with time delay and partly unknown transition proba-bilities.By adding the mode-dependent integral terms of linear Lyapunov-Krasovskii functional,sufficient conditions for L1 boundedness and finite-time L1 boundedness of the systems are proposed.For given L1-gain parameter and finite-time L1-gain parameter,the problem of deriving state feedback controller gain matrices can be converted into the feasibility problem in the form of linear programming.Chapter 6 addresses the problems of positive L1 filter design for positive Markov jump systems and time-delayed positive Markov jump systems with partly unknown transition probabilities.By constructing the linear Lyapunov-Krasovskii functional and the free-connection weighting vectors,sufficient conditions for the existence of positive L1 filter are proposed.For given L1-gain parameter,the problem of deriving positive L1 filter gain matrices can be converted into the feasibility problem in the term of linear programming.Finally,the results of the dissertation are summarized and further research topics are pointed out.