Stability Analysis And Control Of Semi-markov Jump Systems With Saturation

Stochastic switching systems,have significant benefits in modeling the majority of physical systems characterized by abrupt changes since the switching signals between the subsystems are random,and have extensive applications in various fields including speech recognition,weather forecast and mechanical systems.As an important model of stochastic switching systems,semiMarkov jump systems have been vastly researched in recent decades.In the control process of these practical systems,disturbance is an unavoidable influence factor,with the development of control theory,many scholars have proposed some effective anti-disturbance methods,such as robust control,adaptive control,sliding mode control,active disturbance rejection control,observer-based disturbance compensation control,composite hierarchical anti-disturbance control and so on.In this paper,semi-Markov jump systems with generally uncertain transition rates and discrete-time semi-Markov jump systems with incomplete semi-Markov kernel are studied.The research work of this paper is summarized as follows:1.For semi-Markov jump systems with generally uncertain transition rates,the problem of observer-based control is studied in the case of disturbance.Under the unknown state of the system,the design methods of full-order disturbance observer and composite controller are presented,the condition is given to ensure that the closed-loop system is local stochastic stability with H∞ performance level,and the optimal estimation algorithm for the attraction domain of the closed-loop system is given.Finally,the effectiveness of the proposed method is verified by a numerical example.2.For a class of discrete-time semi-Markov jump systems with incomplete semi-Markov kernel,the problem of composite anti-disturbance control based on state observer and disturbance observer are studied.Based on the proposed full observer,a composite controller is constructed,and the conditions of the mean-square stability are expounded.Furthermore,the results obtained are extended to two special cases in which incomplete sojourn-time probability density functions and incomplete transition probabilities.Eventually,the proposed results are verified by three numerical examples.