Stability And Stabilization Of Uncertain Stochastic Markov Jump Systems

Markov jump system is a hybrid system switched according to a random switching ruleamong a set of subsystems. Markov jump systems have been used to describe many practicalsystems, where they may experience abrupt changes in their structure and parameters, such ascomponent failures or repairs, changing subsystem interconnections, and abruptenvironmental disturbances. Moreover, it has been well recognized that uncertainties cannotbe avoided in practice and often results in instability and poor performance. The knowledgeon the transition probabilities are definitely expected to simplify the system analysis.However, the likelihood of obtaining the information of transition probabilities is actuallyquestionable, and the cost is probably expensive. Besides, because of the existence of theenvironmental noise, it is necessary to take this element into account. Therefore, stability andstabilization for the stochastic MJSs, with partly unknown transition probabilities andparameters uncertainties are assumed to be norm-bounded, are very important in controltheory and its applications. This dissertation deals systematically with the stability andstabilization of uncertain stochastic MJSsThe contributions can be concluded as follows:1．Stability and stabilization of continuous stochastic Markov jump systems with partlyunknown transition probabilities are introduced. Necessary and sufficient conditions aredeserved, and state feedback stabilization controller is designed. Then, the design of the staticoutput feedback controller is presented based on singular value decomposition of matrices,and the design problem can be reduced to a set of strict linear matrix inequalities (LMIs)feasibility problem.2．Stability and stabilization of discrete-time stochastic Markov jump systems areresearched. Necessary and sufficient conditions of the systems are given. Then, a statefeedback stabilization controller is designed, and all the design problems are promoted in forms of strict LMIs feasibility problem.3．Stability and stabilization of uncertain stochastic Markov jump systems, withparameters norm-bounded are considered. Necessary and sufficient conditions of the systemsare given, in forms of strict linear matrix inequality. State feedback controller is designed, andthe design problems are reduced to a set of strict LMIs feasibility problem.