Event-Triggered Control And Filtering For Markov Jump Systems

The Markov jump system is an important hybrid dynamic system.It has powerful modeling ability for the mutation phenomenon of system structure or parameter.It is widely used in industrial systems such as circuit systems and network control systems.The singular Markov jump system is a typical hybrid system,which can be regarded as the organic combination of Markov jump systems and singular systems.It has attracted extensive attention in recent years.The semi-Markov jump system is a more general form of Markov jump systems.Compared with the conventional Markov jump system,the sojourn time of the semi-Markov jump system can obey a more general distribution,while that of the Markov jump system only obeys the exponential distribution.Therefore,the semi-Markov jump system has a wider application space than the general Markov jump system,such as the bunch-train cavity interaction systems,cognitive radio network,etc.The control and filtering for Markov jump systems,such as singular Markov jump systems and semi-Markov jump systems,has important theoretical and practical value.In recent years,network communication technology has developed rapidly,and it has also brought a series of challenges,such as network induced delay and data loss,which limits the application of many theoretical research in the network environment.The eventtriggered scheme can reduce the total number of transmitted data and relieve communication pressure via the network,which is an effective means to improve communication quality.In addition,the redundant channel technology can reduces the probability of data loss and improve the reliability of data transmission.These research fields have attracted researchers' great attention.This paper mainly studies the problem of event-triggered control and filtering for Markov jump systems.The physical plants mainly include the singular Markov jump system and the semi-Markov jump system.The event-triggered scheme and the technique of redundant channels has been utilized.Based on H_?control and fuzzy control theories,the corresponding controller or filter is designed.Specifically,the following three problems are investigated: the problem of H_?control for a class of T-S fuzzy singular Markov jump system with redundant channels under a dynamic event-triggered scheme;the problem of H_?filtering for discrete-time singular Markov jump systems with redundant channels under the event-triggered scheme;the problem of reliable mixed H_?/passive control for T-S fuzzy semi-Markovian jump systems under a dynamic event-triggered scheme.Based onthe stochastic Lyapunov-Krasovskii functional and the method of free-weighting matrices,the criterion of stochastically admissible or stochastically stable with a given performance for the closed-loop system is obtained.The corresponding controller or filter is given in the form of linear matrix inequalities.