Non-Fragile Filtering And Fault Detection Of Markov Jump Systems

Markov systems are often used to solve the problem of sudden changes in system param-eters or structure caused by environmental interference,controller failures,and changes in the connection of subsystems.In actual engineering systems,random filter gain fluctuations often occur,which are caused by factors such as rounding errors in data calculations,the length of effective digits,the accuracy of measuring instruments,and digital runoff.In some cases,small gain fluctuations may have a significant impact on the stability of the entire system,and it is often inevitable.Therefore,the designed filter should consider the uncertainty of gain param-eters,that is,non-fragile.At the same time,due to abnormal conditions such as noise signals,transmission data packet loss and delay,and communication failures,the mode of the system will jump and the correct system mode cannot be obtained in time,resulting in inconsistent be-tween system mode and the corresponding filter mode.Asynchronous filters based on hidden Markov models can effectively solve this problemThis paper mainly focuses on discrete Markov jump systems,considering its non-fragile and mode matching,and studying how to design the corresponding filter and meet the perfor-mance index of the system.The main contents are summarized as follows(1)The non-fragile l2-l? asynchronous filtering problem of discrete-time Markov jump systems with time-varying delays is studied.An appropriate method is used to design a non-fragile filter whose mode is asynchronous with the system mode.Sufficient conditions are obtained based on the Lyapunov-Krasovskii functional method,which ensures that the corre-sponding filtering error system is stochastically stable under the specified l2?l? performance indicators.By solving the linear matrix inequalities obtained from the sufficient conditions,the corresponding filter gains are finally obtained.(2)The non-fragile H?,filtering of fuzzy discrete-time systems with Markov jumps and data loss is studied.The Takagi-Sugeno(T-S)fuzzy model is used to represent discrete-time nonlinear systems with Markov jumps.It is assumed that the information transmission from the factory to the filter is imperfect,and a Bernoulli random binary distribution is used to model the phenomenon.A mode-dependent full-order H? non-fragile filter is constructed,which has additional gain changes.Based on the model-dependent Lyapunov function,sufficient condi-tions are established in the form of linear matrix inequalities,so that the corresponding filtering error system has random stability and guarantees the given H? performance index(3)The asynchronous non-fragile fault detection problem of discrete Markov jump sys-tems is studied.Considering the possible gain fluctuation of the fault detector,we designed a non-fragile fault detector.At the same time,in order to make full use of the available mode information of the system,we use the hidden Markov model to describe the asynchronous phe-nomenon of the system.Through Lyapunov function and linear matrix inequality,sufficient conditions for the fault diagnosis system to maintain stochastic stability and strict dissipation are obtained,and a method for solving the gain of the fault detector is given.