The Finite-time Control And Application For Stochastic Markovian Jump Systems

Stochastic Markov jump systems have been a hot topic in the fields of control theory.In practical applications,many dynamic systems whose structures and parameters are subject to random failures or sudden environment changes can be modeled by Markovian jump systems.Examples include networked control systems,power systems,traffic systems and economic systems.On the other hand,finite-time stability has been widely studied due to its significant application in many practical fields,such as aircraft system,robot control system.In this paper,we consider the problems of finite-time control and application for stochastic Markov jump systems.The specific contents are as follows:?1?The problems of finite-time stability and stabilization for stochastic Markov systems are studied by mode-dependent parameter approach.The stability conditions with less conservatism are given.Based on the derived stability conditions,the state-feedback controller and observer-based controller are designed.?2?The problems of finite-time stability and stabilization for stochastic Markovian jump systems with generally uncertain transition rates are discussed.A less conservative stability criterion is presented by a mode-dependent approach.The state feedback and observer-based controllers are designed by a cone complementary linearization method,and two specific algorithms are presented.An example is used to illustrate the merits of proposed approach.?3?The problems of quantitative exponential stability and stabilization for stochastic Markovian jump system are studied.By analyzing the defect of exponential stability definition,the concept of quantitative mean square exponential stability is introduced.And also,the relationship between quantitative exponential stability and finite-time stability is given.Moreover,the state feedback and output feedback quantitative stabilization controllers are designed.?4?The finite-time H₂/H_? control problem for linear It?type stochastic Markov jump system is investigated.By mode-dependent parameter approach,the state feedback and observer-based finite-time H₂/H_? controllers are designed.A precise expression of H₂ cost function is given.