Event-triggered fault detection for discrete-time Markovian jump systems in finite frequency domain

This paper is concerned with the design of the finite frequency fault detection (FD) filter based on the event-triggered scheme (ETS) for discrete-time Markovian jump (DMJ) systems with Lipschitz functions, time-varying delays, and packet dropouts. A novel FD filter subject to ETS and data missing is developed, and the augmented filter system is rewritten as a DMJ-linear parameter varying (DMJ-LPV) system through a reformulated Lipschitz property. Then, two novel lemmas are proposed to guarantee the DMJ-LPV system robust to unknown disturbances and sensitive to finite frequency faults. Next, the proposed lemmas are deduced into linear matrix inequalities by using Finsler's lemma and S-procedure. Finally, the application of Chua's circuit system is employed to illustrate the validity and superiority of the proposed theory.