Research On Fault Detection Method Of Time-delay Markov Jump Systems

With the continuous development of science and technology,large-scale control systems are becoming more and more complex,certain behavior or strict performance requirements of the control system may result in system failure occurs,for the pursuit of the needs of the system safety and performance,how to effectively realize dynamic system fault detection is a key factor that people consider.Due to the sudden change of the environment,the failure of sensors or actuators,resulting in changes in the structure and parameters of the dynamic system,the Markov jump system can be used to model those real dynamic systems affected by sudden changes,so it has received extensive attention.At the same time,due to the aging of components,signal transmission delay and measurement lag,time delay widely exists in the actual Markov jump system,and the occurrence of faults will affect the stability of the actual Markov jump system.Therefore,it has important theoretical value and practical significance to study the fault detection problem of time-delay Markov jump system.Based on Lyapunov stability theory and Linear Matrix Inequality(LMI)technology,the research on fault detection of time-delay Markov jump systems mainly includes:(1)For the discrete time-delay Markov jump systems,the problem of fault detection is studied.Different from the previous situation where all the transition probability matrices are required to be known,studying the case where the transition probability matrix with partially known relaxes the constraints that all the probability matrices are known,and has a wider application range.Based on Lyapunov stability theory and LMI technology,the_?fault detection filter is designed to reduce the error value between residuals and faults,ensure the random stability of the system,and obtain the performance index_?of the Markov jump system.A new summation inequality method and free weight matrix method are used to deal with time-delay,which are less conservative than Jensen's inequality method for time-delay.Finally,the effectiveness of the proposed method is verified by a numerical simulation example.(2)The fault estimation problem of continuous time-delay Markov jump systems with multiple disturbances and actuator faults is studied.Based on disturbance observer,fault diagnosis observer and composite hierarchical controller,the composite control of closed-loop system is realized.The composite control includes two feedforward control and one feedback control.The feedforward control is used to offset multiple disturbances and compensate faults.The feedback control ensures the stability of the closed-loop system,and then obtains the stochastic stability of the composite hierarchical control system.At the same time,a free weight matrix operator is introduced to deal with the time delay,and a smaller conservative result is obtained.Finally,the effectiveness of the proposed method is verified by numerical simulation examples of two actuator faults(sine function,ramp function).