Filtering And Control Analysis Of Markov Jump System With Continuous Time-varying Delay

As a kind of special hybrid system,Markov jump system is often used to describe the dynamic system whose structure is difficult to predict and analyze because of the change of external pressure,the migration of working environment,the artificial change of the system's working breakpoint,the sudden change of the system's internal interrelated State,the damage of working elements and other factors.In the past few decades,with the continuous improvement and development of Markov jump control theory,Markov jump system has been widely used in industry,economy,machine learning,neural network and other fields,so more and more scholars began to study and expand Markov jump system more deeply,which has become one of the hot research areas of control theory.Although the research on the stability of Markov jump system,the design of controller and filter has made a lot of achievements,there are still many problems to be solved.For example:First,most of the existing literature is based on the known or partially known transfer probability when analyzing the stability.In the actual industrial system,due to measurement error or transmission congestion,the transfer probability may have time-varying error.Secondly,most of the existing literature is based on the current input(output)state feedback when designing the controller,ignoring the delay feedback that may exist in the internal information transfer of the controller.Thirdly,most of the existing literature is based on the external noise disturbance in the full frequency domain.Because the information of noise in different frequency bands is not fully utilized,the standard filter obtained has great conservatism.Fourthly,there are few researches on the synchronization control problem and the finite frequency domain control problem of the combination of Markov switching state and neural network.Based on this,aiming at the above problems,this paper deeply studies the stability analysis,the design of parallel distributed compensation(PDC)controller,the design of finite frequency H_?filter,the synchronization control of Markov jump neural network and the control of finite frequency domain.In the framework of Lyapunov stability theory and linear matrix inequality,a series of effective analysis and methods are proposed.The main work is summarized as follows:First,before studying the design of controller and filter,it is necessary to analyze the stability of Markov jump system.For continuous Markov jump systems with standard time-varying delays,sufficient conditions for stochastic stability are obtained by using Lyapunov-krasovski functional and improved Wirtinger inequality method.For continuous Markov jump systems with time-varying transition probability,sufficient conditions for stochastic stability under the disturbance of time-varying transition probability are obtained by Lyapunov-krasovski functional and improved interactive convex inequality method.In addition,the optimization of positive definite conditions of Lyapunov-krasovski functional is also discussed.Secondly,on the premise of stochastic stability of Markov jump system,the design of PDC controller and H_?filter are studied respectively.For the design of PDC controller,sufficient conditions for the stochastic stability of the closed-loop system are obtained by using Lyapunov-krasovski functional and Bessel-Legendre inequality.To solve the problem of H_?filter design,the standard full frequency domain H_?filter and the finite frequency domain H_?filter are designed by using the improved Wirtinger inequality method,the generalized KYP lemma and the Projection Lemma.Thirdly,as an extension of Markov jump control theory,the analysis and design of the combination of Markov switching state and neural network are studied.Firstly,based on the sample point controller,the sufficient conditions for the complete synchronization of the drive system and the response system of Markov jump neural network with uncertain parameters and mixed time-varying delays are established,and the optimization of time-varying delays in two-dimensional space is also studied.Secondly,for the control problem of Markov jump neural network with mixed time-varying delay under the disturbance of finite frequency domain,the PDC controller is designed to make the closed-loop system stochastic stable.