Robust non-fragile H∞ fault detection filter design for delayed singular Markovian jump systems with linear fractional parametric uncertainties

Abstract

Abstract This paper investigates the problem of non-fragile H ∞ fault detection filtering for a class of uncertain time-varying-delay singular Markovian jump systems (SMJSs). Linear fractional parameter uncertainties are considered and the designed filter is supposed to contain gain variations. The main objective is to design a mode-dependent non-fragile fault detection filter to guarantee the fault detection system to be stochastically admissible with an H ∞ performance index for all admissible uncertainties. First, by constructing a novel mode-dependent stochastic Lyapunov–Krasovskii functional and employing integral inequality approach, sufficient delay-dependent conditions on stochastic admissibility and H ∞ performance analysis for the fault detection system are presented in terms of linear matrix inequalities (LMIs). Then, the existence conditions of the desired fault detection filter and the explicit expressions for calculating the filter parameters are established. Finally, a numerical example and a DC motor are employed to show that our methods are effective.