Resilient fault detection observer design of fuzzy Markovian jumping systems with mode-dependent time-varying delays

This paper studies the resilient fault detection observer (FDO) design problem for a class of T-S (Takagi-Sugeno) fuzzy Markovian jumping systems (MJSs) with mode-dependent time-varying delays. Based on the T-S fuzzy models, the dynamics of mode-dependent resilient FDO and the overall T-S fuzzy dynamic MJSs are constructed. By selected the appropriate Lyapunov-Krasovskii functional, a sufficient condition is obtained to guarantee the stochastic stability of the overall T-S fuzzy dynamic MJSs. Meanwhile, taking into account the robustness against unknown disturbances while guaranteeing the sensitivity to faults, the H∞ performance index is proposed to minimize the influences of the unknown disturbances and the H− performance index is introduced to enhance the sensitivity to faults. By means of linear matrix inequalities (LMIs) techniques, the sufficient condition on the existence of the resilient FDO are respectively presented and proved. And the designed problem is then formulated as a two-objective optimization algorithm. A numerical simulation is given at last to illustrate that the proposed resilient FDO can detect the faults shortly after the occurrences without any false alarm.