Fault Detection Filter Design of Polytopic Uncertain Continuous-Time Singular Markovian Jump Systems with Time-Varying Delays

Abstract

This paper investigates the problem of full-order and reduced-order fault detection filter (FDF) design under unified linear matrix inequality (LMI) conditions for a class of continuous-time singular Markovian jump systems (CTSMJSs) with time-varying delays and polytopic uncertain transition rates. By constructing a new Lyapunov function, sufficient conditions are firstly provided for the singular model error augmented system such that the system is stochastically admissible with an H∞ performance level γ. And then, by applying a novel convex polyhedron technique to decoupled linear matrix inequalities, the full-order and reduced-order fault detection filter parameters can be obtained within a convex optimization frame. The reduced-order fault detection filter (FDF) can not only meet the fault detection accuracy requirements of complex systems but also improve the fault detection efficiency. Finally, a DC motor and an illustrative simulation example are given to verify the feasibility and effectiveness of the proposed algorithms.

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

“…Over the past few decades, MJSs have attracted much attention and a lot of relevant results have been reported (Li et al, 2015; Li et al, 2016; Shen et al, 2019; Wei et al, 2017; Wei et al, 2017b). Therefore, the study of singular Markov jump systems is of great significance and value both theoretically and practically; as a hot topic, many results have also been shown (Feng and Lam, 2013; Ma et al, 2018; Park et al, 2019; Shi and Peng, 2020; Wang et al, 2015; Zhang et al, 2014; Zuo et al, 2018). It is worth noting that in most of the current researches on singular Markov jump systems, the focus on TRs in the Markov process is assumed to be known and unknown, and few people consider the case of TRs being polytopic uncertain.…”