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H ∞ Fault Detection for Two‐Dimensional T ‐ S Fuzzy Systems in FM Second Model
Author(s) -
Wang Lanning,
Wang Weiqun
Publication year - 2015
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.892
Subject(s) - fault detection and isolation , fuzzy logic , filter (signal processing) , control theory (sociology) , fault (geology) , mathematics , sensitivity (control systems) , computer science , algorithm , engineering , artificial intelligence , electronic engineering , control (management) , seismology , actuator , computer vision , geology
This paper investigates the H ∞ fault detection problem for two‐dimensional (2 D ) Takagi‐Sugeno ( T ‐ S ) fuzzy systems in a Fornasini‐Marchesini second ( FM II ) state‐space model. Our aim is to develop fault detection filters for the 2 D T ‐ S fuzzy system both in the non‐fuzzy case and the fuzzy case. Attention is focused on the design of the above two kinds of fault detection filters, which guarantee the fault detection system to be asymptotically stable and to have a prescribed H ∞ performance. Sufficient conditions are derived for the existence of such filters in terms of linear matrix inequalities ( LMIs ), and the corresponding filter synthesis problem then is solved both of the kinds of fault detection filters. Numerical examples are used to demonstrate the effectiveness of the proposed method. Moreover, simulation results show that, under the conditions of reaching the same optimal H ∞ performance level and feasible region, the fault detection filter we designed for the fuzzy case has better sensitivity to the fault signal than the one designed for the non‐fuzzy case.