Asynchronous Fault Detection Filter for Discrete Singular Markov Jump Systems via Event-Triggered Scheme

This paper discusses the asynchronous fault detection filter (FDF) problem for discrete singular Markov jump systems (SMJSs) via event-triggered scheme (ETS). A hidden Markov model (HMM) is adopted to describe the asynchronization behavior between the system and the FDF. An event-triggered scheme (ETS) is used to reduce the cost of calculation. Moreover, the FDF is designed to detect when the failure occurs to the system. Firstly, sufficient conditions are given to assure that the system is stochastically admissible (SA) with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty } $ </tex-math></inline-formula> performance. Secondly, based on the linear matrix inequality technique (LMI), the FDF and the event-triggered parameters are designed. Finally, a dynamic Leontief model of economic systems (DLMES) is verified to show the usefulness of the design method.