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Fuzzy model-based fault detection for Markov jump systems. (English) Zbl 1166.93343
Summary: The Robust Fault Detection Filter (RFDF) design problems are studied for nonlinear stochastic time-delay Markov jump systems. By means of the Takagi-Sugeno fuzzy models, the fuzzy RFDF system and the dynamics of filtering error generator are constructed. Moreover, taking into account the sensitivity to faults while guaranteeing robustness against unknown inputs, the $H_\infty $ filtering scheme is proposed to minimize the influences of the unknown inputs and another new performance index is introduced to enhance the sensitivity to faults. A sufficient condition is first established on the stochastic stability using the stochastic Lyapunov-Krasovskii function. Then in terms of linear matrix inequalities techniques, sufficient conditions on the existence of fuzzy RFDF are presented and proved. Finally, the design problem is formulated as a two-objective optimization algorithm. Simulation results illustrate that the proposed RFDF can detect the faults shortly after the occurrences.

93C42Fuzzy control systems
60J75Jump processes
15A39Linear inequalities of matrices
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