Fault detection filter design for a class of nonlinear Markovian jumping systems with mode-dependent time-varying delays

The fault detection filter (FDF) design problem of a class of time-delayed and nonlinear Markovian jumping systems (MJSs) is considered. The delays in this paper are mode-dependent and time-varying. Using the Takagi–Sugeno fuzzy (TSF) modeling methods, the relevant TSF-MJSs related to the TSF-FDF model are obtained. Through introducing a reference residual model, the FDF design scheme can be derived as an $H_{\infty }$-filtering formulation. By selecting a suitable mode-dependent time-delayed Lyapunov–Krasovskii functional (LKF), we get sufficient conditions through which the stochastic stability of the TSF-MJSs can be guaranteed. Then in terms of linear matrix inequalities techniques, the fuzzy FDF design scheme can be derived as an optimization one. A simulation example is demonstrated as last to illustrate the feasibility of the studied methods.