Fault Detection Filtering For Markovian Jump Singular Systems Via Event-triggered Technique

During system operation,there will be some sudden events,such as damage to individual components of the system,sudden changes in system parameters,and generation of external disturbances.The occurrence of such events is likely to lead to changes to the system structure,which in turn affect its stability,even leading to the collapse of the entire system,and ultimately resulting in reduced efficiency or even safety incidents in the production process.Therefore,research on improving the system's fault detection has important practical significance.In addition,the Markovian jump system,as a type of stochastic hybrid system,can describe a wide range of systems and has significant practical value.Although the fault detection of the Markovian jump system is highly universal,its accuracy and effectiveness still need to be improved.Thus,in this paper,the fault detection of the Markovian jump system is studied in more depth from the following two aspects:Firstly,for the accuracy of the Markovian jump system fault detection,the fault detection problem of a singular Markovian jump repeated scalar nonlinear system is studied.For a given singular Markovian jump repeated scalar nonlinear system,necessary and sufficient conditions for the system to be stochastically admissible are proposed.The positive diagonally dominant Lyapunov function approach is used to obtain the conditions under which the system is stochastically stable with the guaranteed performance index.Then,based on the obtained stochastically admissible conditions,the existence conditions for the fault detection filter such that the system satisfies the optimum performance are derived.Finally,the feasibility of the designed fault detection filter is verified by simulation examples.Secondly,for the effectiveness of Markovian jump system fault detection,the fault detection problem of a Markovian jump system based on an event-triggered scheme is studied.By using Lyapunov function approach,it is proved that the design method proposed in this thesis can ensure the stochastic stability of the control systems.Using the optimized signal transmission method based on the event trigger mechanism,the existence conditions of the fault detection filter that satisfy the desired performance are given.The superiority and effectiveness of the design scheme are verified by simulation examples.In addition,by comparing the data transmission effects under different event-triggered parameters,the impact of event-triggered parameters on data transmission efficiency is analyzed,and the advantages of the event-triggered scheme in improving system transmission efficiency and reducing system resource consumption are verified.The results of this research paper will provide an important contribution to the literature for improving the accuracy and effectiveness of the Markovian jump system fault detection problem.It has important practical significance for improving the probability that the real system will avoid faults.