Finite-time Annular Stability And Stabilization Of Stochastic Markov Jump Systems

It is well known that simple deterministic systems can no longer meet the needs of engineering,because many dynamic systems are inevitably affected by various noise during operation,which makes the structure and state of the system change.However,the stochastic Markov jump system can be used to describe such phenomena because of its continuous change of state variables.In addition,most of the research results on the stability of stochastic systems focus on the Lyapunov asymptotic stability,that is,in an infinite period of time,the system can become stable.However,this certainly does not meet the actual operating conditions.In fact,under the interference of some uncertain factors,stochastic systems often have transient characteristics that break the threshold within a limited time interval.In order to study the transient performance of the system,the stochastic Markov jump system is studied in this thesis,and the details are as follows:(1)The finite-time annular domain stability and stabilization are studied for the nonlinear impulsive stochastic Markov jump systems with Wiener and Poisson noises.Firstly,the definition of finite-time annular domain stability in probability is introduced.Secondly,based on the concept of finite-time annular domain stability in probability,the stability theorem of finite-time annular domain stability in probability is derived by using the inverse technique of Lyapunov function and Markov inequality.Then,an appropriate state feedback probabilistic stabilizing controller is designed,and the set of possible control laws is given.Finally,a numerical example is given to verify the effectiveness of the proposed method.(2)For hidden Markov switching systems with Wiener and Poisson noises,the asynchronous finite-time annular domain stability and stabilization are studied.Firstly,the hidden Markov switching system is introduced to describe the asynchronous phenomenon that the system mode is not synchronized with the controller mode.Secondly,the definition of mean square finite-time annular domain stability is extended,and a more general concept of generalized mean square finite-time annular domain stability is obtained.Then,the asynchronous finite-time annular domain stability theorem and the state feedback stabilizing controller are designed by using the single optimal variable separation parameter method.Subsequently,a half-interval search algorithm is designed to solve the asynchronous finite-time annular domain stability condition with N mode,which greatly improves the processing speed of the algorithm.Finally,a numerical example is given to verify the validity of the proposed theorem.