On Designing H_? Filter And Memory State Feedback Controller For Nonhomogeneous Markov Jump Systems With Time-delay

Markov jumping systems can solve the problem of jumping characteristics of system structural parameters caused by internal component failure or environmental disturbance in the process of practical production and application.In recent years,Markov jump systems are a hot topic in current system research.At present,most of the studies on Markov jump systems and the transfer probabilities in related literatures are time-invariant,such as fully known,fully available upper and lower bound information,partly unknown,and so on.However,for practical engineering,time-varying is inevitable,so the study of time-varying transition probability(non-homogeneous Markov chain)is particularly important.On the other hand,in practical applications,time-delay is inevitable.Therefore,in recent years,systems with time-delay are worth studying,which further make the comprehensive analysis of time-delay Markov jump systems become a hot research topic in the field of control.Therefore,this thesis summarizes the existing research results,and further discusses the design of controllers and filters for time-delay nonhomogeneous Markov jump systems.The details are as follows:1.The first chapter mainly introduces the basic concepts,research status and research significance of Markov jump systems,and introduces the time-delay systems and H? filtering.Finally,this paper introduces the research idea and main work.2.The second chapter is concerned with the H? filter design for a class of nonhomogeneous Markov jump systems with time-delay.The time-varying transition rate matrix in continuous-time domain is considered to be in a convex bounded domain.The filter is designed.The condition of random stability is obtained by constructing a Lyapunov functional and introducing a free weight matrix.The parameters of the filter are obtained.Finally,a set of numerical examples are given to illustrate the effectiveness of the method.3.The third chapter considers the problem of non-fragile and mode-dependent filter design for a class of uncertain nonhomogeneous Markov jump systems with time-varying delay and time-varying transition rates.The time-varying transition rate matrix in continuous-time domain is considered to lie in a convex bounded domain.The non-fragile and mode-dependent filter to be designed is assumed to include multiplicative gain variations which result from inaccuracies in filter implementation.By constructing Lyapunov-Krasovskii function,the required filter can ensure that the filtering error system not only satisfies stochastically stability,but also satisfies the prescribed H? norm level for all admissible uncertainties.Finally,a set of numerical examples is given to illustrate the effectiveness and less conservatism of the method.4.The fourth chapter studies the design of memory state feedback controller for linear Markov jump systems.By constructing a set of Lyapunov functions and using a new interval fraction method,we obtain a set of less conservative stability conditions for delay-dependent matrix inequalities with time-varying parameters,and then use the convex property to transform them into solvable linear conditions,which improves and broadens some existing conclusions.In the process of controller synthesis,by introducing a lower delay state,the historical information of the system is taken into account in the controller design.The last two sets of numerical examples illustrate the effectiveness and less conservatism of the method.5.Summary and Prospect of this paper.