Fault Detection Of Positive Markov Jump System

As the complexity of the system continues to increase,there are various types of interference,modeling errors,time-delay and other factors.If the system fails,it may cause heavy casualties and property losses.Therefore,the system fault detection is particularly important,its main role is to determine whether the system or components work abnormal.These dynamic systems affected by random mutations can be modeled as positive Markov jump systems.This paper studies the fault detection of positive Markov jump systems based on the state estimation method of analytical models.In this paper,the fault detection problem is transformed into a filtering problem,and the fault detection problem is emphasized from two aspects of disturbances and time-delay.The first chapter mainly introduces the research background and research status of fault detection and positive Markov jump system.And it shows that the research topic of this paper is fault detection of positive Markov jump system.The second chapter introduces the preliminary knowledge,relevant definitions,theorems and concepts in this study.The third chapter studies the fault detection problem of positiveMarkov jump systems with disturbances.A continuous-time positive Markov jump system model is established for the system fault problem,and the residual generator is designed.In this way,the fault detection problem is transformed into the design problem of a positive L₁ filter.By studying the stochastic stability and L₁ gain performance,the influence of interference on the residual error is reduced to make the system meet the performance requirements.Finally,the solution of the fault detection filter parameters is obtained by linear programming.Then the residual output value is compared with the predetermined threshold to determine the system fault state,and the fault detection of the positive Markov jump system with disturbance is finally completed.The fourth chapter studies the fault detection problem of positive Markov jump systems with time-varying delays.In order to solve the problem of fault detection for a positive Markov jump system with time-varying delays,firstly,a robust fault detection filter is constructed.Secondly,the multiple co-positive type Lyapunov-Krasovskii functional is constructed by adding the first integration term and the second integration term.The weak infinitesimal operator is defined and Dynkin's formula is applied to obtain the conditions for the stochastic stability of the system.Thirdly,by introducing free weight vector,the system conservatism is reduced,and the performance and stochastic stability are analyzed.The linear programming method is applied to the positive jump system,and the parameterized matrix of the filter is constructed to establish sufficient conditions for the existence of the filter.Finally,the validity of the method is verified by simulation experiment.The problem of fault detection for a positive Markov jump system with variable time delay is solved.Finally,it is a summary of the content of this article and the planning of future research directions.