Stability Analysis And Fault-Tolerant Control Of Time-Delay Markov Jump Systems

In the actual production process,the system working for a long time may cause the system parameter jump,or even failure,and then destroy its stability.At the same time,time delay is a common problem in all kinds of practical systems.In view of the above situation,based on controller reconstruction and finite time stabilization method,this paper studies the stability analysis and fault-tolerant control of stochastic Markov jump delay systems,so as to enhance the stability and fault-tolerant ability of the controlled system.The research content mainly includes the following three aspects :(1)stability analysis and controller design of markov jump time-delay systems based on energy peak control.The uncertainty of external disturbance and the system time delay easily lead to the state response of the system exceeding a certain limit,which leads to the degradation of system performance and even instability.Energy peak control can effectively ensure the stability of the system under the action of a certain disturbance energy,and the state response does not exceed a given limit.By constructing Lyapunov functional and solving it based on matrix inequality,we obtain the related theorem of energy peak stability for Markov jump delay systems,and demonstrate its validity by examples.(2)Stability analysis and controller design of Markov jumping time-delay systems based on finite time stability.Based on the comprehensive mathematical model of Markov jump delay systems,the theory and method of finite time stability control different from Lyapunov asymptotic stability are studied,and the related theorems are obtained.The solution of the theorem can effectively ensure that under certain initial conditions,the state response of the system will not exceed a certain range in a finite time,and ensure that the system is within the safety boundary,which has a certain practical significance.The related methods can be easily generalized to other types of systems.(3)Fault-tolerant control method and controller reconfiguration technology for Markov jump delay systems.The actual system runs for a long time,which inevitably leads to errors.Based on the mathematical model of system error and the research results of finite time stability of Malkov jump delay systems,the error calculation method of system is discussed and the system error detection is realized.For minor or undetectable errors(such as sensor errors and driver errors),a robust controller is designed to meet the fault-tolerant control requirements of the system.For serious errors,the controller reconstruction method and controller switching strategy are studied based on the theory of finite time stability.By means of the finite time stability theory,the range of state change during controller switching is limited,which ensures the safety and stability of the system during controller switching.The results obtained in this paper can effectively ensure the stability of markov jump time-delay systems and make them fault-tolerant,and the relevant theorems can be easily extended to other types of system analysis and controller design.