Fuzzy Filter Design for ItÔ Stochastic Systems With Application to Sensor Fault Detection

The paper deals with the robust fault detection problem for Takagi–Sugeno (T--S) fuzzy ItÔ stochastic systems. Our aim is to develop a robust fault detection approach to the T--S fuzzy systems with Brownian motion. By using a general observer-based fault detection filter as a residual generator, the robust fault detection is formulated as a filtering problem. Attention is focused on the design of both the fuzzy-rule-independent and the fuzzy-rule-dependent fault detection filters guaranteeing a prescribed noise attenuation level in an ${{\H}}_\infty$ sense. Sufficient conditions are proposed to guarantee the mean-square asymptotic stability with an ${{\H}}_\infty$ performance for the fault detection system. The corresponding solvability conditions for the desired fuzzy-rule-independent and fuzzy-rule-dependent fault detection filters are also established. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.