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

Abstract 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.