Sliding Mode Control For Markov Jump Systems

In realistic systems,there often exist the structural changes caused by component failures,changes of environment,parameter changes and internal correlation changes of subsystems.These changes can be described via Markov jump systems.Therefore,in the framework of Markov jump,this thesis studies the sliding mode control of observer based Markov jump systems,Semi-Markov jump systems and singular Semi-Markov jump systems.Firstly,observer based sliding mode control is studied for nonlinear Markov jump systems with time-varying delays and disturbances.A non-fragile observer is designed to estimate the unmeasurable states,nonlinear functions and actuator failures.The integral sliding surface and sliding mode controller are designed based on the above observer.By using Lyapunov function,Jensen inequality and one-sided Lipschitz method,the sliding mode dynamic systems can be stable with mixed H_? and passive performance index,and the state of the systems can reach the sliding mode surface in finite time.Numerical examples are given to illustrate the feasibility of the theory.Then,the Semi-Markov jump systems are studied,and the adaptive sliding mode control is designed based on the observer,the Lyapunov function with mode dependence and triple integral term is designed.The Newton-Leibniz formula,writinger inequality and integral inequality with mode dependence in stochastic term are combined to reduce the complexity of calculation.By solving the linear matrix inequalities,the feasibility solution is obtained,and the sufficient condition for the closed-loop systems to be asymptotically stable is obtained,and the performance index of mixed H_? and passive is satisfied.The validity of the theory is verified by a numerical example.Finally,the observer based adaptive sliding mode control for singular uncertain SemiMarkov jump systems is studied.A compensator is designed to reduce the influence of nonlinear functions on the systems,and the unknown parameters of function are estimated by adaptive law.Based on Lyapunov function,sufficient conditions for stochastic admissibility of sliding mode dynamic systems are obtained.An observer based adaptive sliding mode control law is proposed to make the trajectory of the system reach the sliding mode surface in finite time.The effectiveness of the theory is proved by a simulation example.