Sliding Mode Control For Stochastic Time Delay Systems

The Markov jump system is a kind of stochastic system with multi-modality,the sys-tem describes the transition law of the system between different modes through a set of s-tochastic Markov chains,and the transition probability does not change with time.However,the transition law of the Semi-Markov jump system can change with time.This paper stud-ies the sliding mode control problem of normal Markov jump system,Semi-Markov jump system and singular Markov jump system,and considers random uncertainty,time-varying delay,input saturation,nonlinear function and the effect of external disturbances on its sys-tem.The main contents of this paper are as follows:Firstly,the sliding mode control of the singular time-delay Markov jump system is s-tudied,the uncertainties which occur randomly are considered.By designing the appropriate sliding surface function,sliding mode controller,and constructing the Lyapunov function,the sliding mode dynamic system is exponentially stable,and the appropriate sliding mode controller makes the state trajectory of the system can reach the set sliding surface in a finite time.By solving the linear matrix inequality,the corresponding gain matrix and the H?performance index are obtained.Secondly,the Markov jump system is extended to the Semi-Markov jump system,and input saturation and time-varying delay are considered.The time-varying delay and nonlin-ear function occur randomly,and the random variables have correlation.An integral sliding surface function,a sliding mode controller and a suitable Lyapunov function are designed to make the sliding modal system asymptotically stable.Finally,the sliding mode control of Markov jump time-delay systems is studied,but the transition probability of the system is partially unknown.The dimension of the system is reduced by the reduction order processing.By designing linear sliding surface function and the suitable Lyapunov function,the sliding modal system is asymptotically stable.At the same time,the sliding mode controller is designed to make the state trajectory of the system reach the sliding surface in a limited time.