Analysis And Synthesis Of Control Strategies For Several Kinds Of Markov Jump Systems

With the rapid development of information technology,related control theory is becoming mature,and the network control technology has been used to solve industrial problems in production.However,these practical problems are often complicated,usually caused by environmental changes,component damage,subsystem interconnection and other factors.In view of this phenomenon,Markov jump system,as a multi-mode random hybrid system with a unique mechanism,can accurately model the actual system,which provides a new choice for the realization of automatic control,and it has high research value.Therefore,this paper studies the control strategies of several kinds of Markov jump systems under complex working environments from different perspectives.Relevant research contents are concluded as follows:1.For a class of nonlinear Markov jump systems based on T-S fuzzy model,the problem of extended dissipative fault-tolerant control is solved.Markov process is used to describe the variation of structural parameters in the system,and a series of white sequences subject to Bernoulli distribution is used to describe the phenomenon of random gain variation.Compared with the existing researches,two different control methods are integrated to design the system controller on the basis of fully considering the mode switching of the controller.Meanwhile,based on Lyapunov stability theory,a set of sufficient conditions for the closed-loop system to achieve mean square stochastic stability and satisfy an extended dissipation performance index are given.Finally,the effectiveness of the proposed method is verified by a numerical example.2.For a class of discrete hidden Markov jump systems,the problem of static output feedback security control under replay attack is solved based on multi-sensor scheme.Firstly,based on hidden Markov knowledge,the system in which the controller mode and the system mode are asynchronous is established,and the robustness of the system is quantified by introducing a H_∞indicator.Secondly,a new detection scheme is designed,which can make the system detect all replay attacks under the premise of maintaining stability,and eliminate the negative effects caused by these attacks.Then the Lyapunov function is separated from the product of the input/output matrix and the controller gain by using the scaling technique of the correlation inequality,which eliminates the coupling relationship between them.In addition,this chapter also gives a set of sufficient conditions for the system to remain stable and meet a H_∞index regardless of whether the system is subjected to replay attacks,the effectiveness of the design method is well verified by a numerical example.3.For a class of discrete Markov jump systems based on T-S fuzzy model,the problem of static output feedback security control when the system is subjected to replay attack is solved.Firstly,according to stochastic theory and T-S fuzzy model,a system in which the controller mode and the system mode are asynchronous is established.Secondly,a detection scheme has been designed to enable the system to detect all replay attacks while maintaining stability and remove the negative impact induced by replay attacks.Then,the constraint that the input and output matrices must be full rank of column and column is removed by the scaling technique of correlation inequality,which greatly reduces the conservatism of controller design.Finally,a set of sufficient conditions for the system to remain stable and satisfy one index regardless of whether the system is subjected to replay attack are given.The effectiveness of the design method is well verified by a numerical example.