Fault detection for nonlinear multirate systems with time-varying delays under a hybrid dynamical event-triggered scheme

Abstract

This paper considers the fault detection (FD) problem for a class of nonlinear multirate systems (NMRSs) with time-varying delays. Here, in order to preserve more effective information and simplify calculations, a new compensation method is utilized to unify the rates of multirate systems (MRSs). On the other hand, a novel hybrid dynamical event-triggered scheme (HDETS) is proposed to regulate the frequency of signal release by adding an adaptive switching multiplicative variable (ASMV) on the basis of dynamic event-triggering mechanism (ETM). Specifically, the ASMV of the triggering function will switch based on the feedback information of FD. In addition, by adjusting the parameters of the triggering function, the triggering condition can be flexibly adjusted to control the triggering rate. The aim of this paper is to design an HDETS-based fault detection filter (FDF), which guarantees that the augmented system is asymptotically stable (AS) with prescribed $H_{\infty }$ performance. Next, the gains of FDF are derived through linear matrix inequality (LMI). Finally, two examples of the ballistic roll rate system and Chua’s circuit system are performed to verify the effectiveness of the FDF designed under HDETS.