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Zbl 1166.93343
He, Shuping; Liu, Fei
Fuzzy model-based fault detection for Markov jump systems. (English)
[J] Int. J. Robust Nonlinear Control 19, No. 11, 1248-1266 (2009). ISSN 1049-8923

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.

MSC 2000:: *93C42 Fuzzy control
60J75 Jump processes
15A39 Linear inequalities

Keywords: robust fault detection filter (RFDF); Takagi-Sugeno fuzzy models; Markov jump systems; linear matrix inequalities

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Zentralblatt MATH Berlin [Germany]