Sliding Mode Control For Singular Markov Jump Systems

Markov jump system can describe the problem that the change of external environment leads to the sudden change of system structure.Compared with the general actual system,the singular system can better maintain the physical characteristics of the system in the actual system,so it has a wider range of applications.Singular Markov jump system models exist in many practical systems,such as circuit systems,economic systems and network systems.Therefore,the study of singular Markov jump systems has important theoretical significance.On the other hand,sliding mode control has the characteristics of insensitive to disturbance and simple calculation,which plays an important role in the research of control system.Due to the limited communication bandwidth,there will be problems such as network congestion and delay.Introducing event-triggered strategy to solve this problem has important theoretical and practical significance.In this paper,the sliding mode control problem of singular Markov jump systems under event-triggered strategy is studied.The specific research contents are as follows:Firstly,an asynchronous sliding mode controller is designed for singular Markov jump systems under event-triggered strategy.The hidden Markov model is used to describe the phenomenon that the system mode and the controller mode are not synchronized.The eventtriggered strategy based on sampling is proposed.The asynchronous sliding mode control law is obtained by combining the event-triggered strategy,and the appropriate Lyapunov function is constructed.The criterion of stochastic admissibility of the closed-loop system is given by using linear matrix inequality.Secondly,the design method of sliding mode controller for a class of uncertain singular Markov jump systems with time-varying delay under dynamic event-triggered strategy is studied.A dynamic event triggering strategy related to the system output information is designed,and an observer based on the triggering output measurement is proposed to reconstruct the state vector.Based on the mode-dependent Lyapunov function,sufficient conditions for stochastic admissibility,mixed passivity and H∞ performance of the closed-loop system are established.Finally,the asynchronous sliding mode control problem of singular Markov jump systems under network attacks is studied.An adaptive event-triggered strategy is designed to reduce signal transmission.Considering the spoofing attack,an integral sliding mode surface is designed to ensure the condition of stochastic stability of the singular Markov jump system.On this basis,the integrated asynchronous sliding mode control law ensures the reachability of the system state trajectory.