Finite-Time Fault Detection and $$H_\infty $$ State Estimation for Markov Jump Systems Under Dynamic Event-Triggered Mechanism

Abstract

AbstractThis chapter addresses the problems of finite-time fault detection (FD) and \(H_\infty \) state estimation for event-triggered discrete-time Markov jump systems under hidden Markov mode observation. A new dynamic event-triggered mechanism is proposed to reduce unnecessary data transmissions so as to save limited network resources. The modes of the Markov jump system are observed by the FD filter (FDF) and the state estimator obeying a hidden Markov process. By constructing Markov-mode-dependent Lyapunov functions, sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained under which the filtering error system of FD and the estimation error system of state estimation are stochastically \(H_\infty \) finite-time bounded. The parameters of the FDF and state estimator are designed when these LMIs are feasible. Two numerical examples are given to verify the effectiveness and merits of the designed FDF and state estimator.KeywordsFault detectionFinite-time \(H_\infty \) state estimationMarkov jump systemsDynamic event-triggered mechanismHidden Markov model