Analysis And Design Of Markov Jump Systems With Piecewise-constant Transition Rates

As a special stochastic system,Markov jump system has been widely used in various practical engineering fields,and has received increasing attention.Because of the influence of environment and device failures,the transition possibilities between modes maybe vary in real systems.In addition,there are a large number of random physical phenomena in reality,such as random temperature changes,component failures,sensor saturations,transmission delays,and so on,which will degrade the performance of the systems and even lead to instability.Therefore,it is of great theoretical value to study Markov jump systems with piecewise-constant transition possibilities,random nonlinearities and random delays.This thesis focuses on analysis,control and filtering of Markov jump systems with piecewise-constant transition possibilities,random nonlinearities and delays.The main con-tents of this thesis are given as follows:In the first part,the static output feedback control problem of Markov jump systems with piecewise-constant transition possibilities,random nonlinearities and random delay is inves-tigated.Based on the average dwell time technique and Lyapunov functional method,the s-tochastic stability of the closed-loop system is analyzed.Then,the parameter matrices of the static output feedback controller in terms of strict linear matrix inequalities(LMIs)are obtained by singular value decomposition(SVD)method.In the second part,the H? filtering problem for Markov jump systems with piecewise-constant transition possibilities,random sensor nonlinearities and random delay is addressed.This part considers the random sensor nonlinearities.Based on the average dwell time method and Lyapunov stability theory,the sufficient condition is obtained to guarantee the augmented filtering error system to be stochastic stability with given Hx performance.Then,the gain matrices of the filter are obtained by solving some LMIs.In the third part,the passivity control problem for Markov jump systems with piecewise-constant transition possibilities,random nonlinearities and randorn sensor delays is investigated Different from the first two parts,this part investigates sensor delay with known probability dis-tribution.Based on the average dwell time method and Lyapunov stability theory,the sufficient stochastic passivity condition is presented.Then,the parameter matrices of the observer-based controller are obtained by the SVD technique.In the fourth part,the summary and further directions are given.