Stability Analysis And Asynchronous Control Of Markov Jump System

Markov jump system known as a special kind of stochastic hybrid systems,which con-sists of two parts:the state mode and the system mode.Its feature is to better simulate the sudden change of dynamic system structure,such as environmental mutation,association change of subsystems,components damage of the system and human intervention.With such excellent performance,the related research on Markov jump system model has always been a hot issue in the field of control.Therefore,this paper focuses on Markov jump system model.The specific work is as follows:Firstly,the observer-based asynchronous control for Markov jump system with time-varying delay and disturbance is discussed.A mixed observer is proposed to estimate the state and disturbance that cannot be measured.The estimated compensator has the ability to compensate the effect of disturbance.Based on the above observer,an asynchronous controller can be constructed to handle the asynchronous phenomenon of the system mode and the controller mode.By applying a complex Lyapunov functional,convex combination and Writinger inequality,some sufficient conditions are obtained to ensure that the original system with an H_? performance and the error systems achieve asymptotic stability.Two examples are provided to illustrate the effectiveness of the technology.Secondly,based on the state observer,the adaptive asynchronous sliding mode control of nonlinear Markov jump system is studied.Mapping the nonlinear system into a class of linear system through the T-S fuzzy model.A non-fragile observer which has norm-bounded gains is adopted to calculate the system state.Based on the non-fragile observer,designing the integral sliding mode surface and asynchronous controller,and obtaining the sufficient conditions for the asymptotic stability of the integrated system with the performance index of H_?.In addition,an adaptive asynchronous sliding mode law is proposed to make the system state trajectory reach the sliding mode surface in a finite time.Two examples are used to illustrate the practicality of the technology.Finally,the problem of event-triggered-based asynchronous sliding mode control for an interval type-2 fuzzy singular Markov jump system is considered.The asynchronous sliding mode control problem of T-S fuzzy Markov system is extended to the interval type-2 fuzzy singular Markov jump system.A state-based event trigger mechanism and the threshold are given,and then a sufficient condition for mean square exponential stability of the sys-tem is obtained by combining event trigger condition,sliding mode law and asynchronous controller.An example is used to illustrate the correctness of the technique.