Fault Detection Filtering for Uncertain Itô Stochastic Fuzzy Systems With Time-Varying Delays

This paper considers the problem of robust $$H_{\infty }$$H∞ fault detection for a class of Itô stochastic Takagi–Sugeno fuzzy systems with time-varying delays and parameter uncertainties. The purpose is to design fuzzy-rule-independent and fuzzy-rule-dependent fault detection filters, which guarantee the fault detection system is not only mean square asymptotically stable, but also satisfies a prescribed $$H_{\infty }$$H∞-norm level for all admissible uncertainties. Via the application of Lyapunov stability theory and the linear matrix inequality technique, novel delay-dependent solvability conditions are obtained. Weighting fault signal approach is utilized to improve the performance of the fault detection system, and explicit expression of the desired filter parameters is characterized by congruence transformation, matrix decomposition, and convex optimization technique. A numerical example and a mass-spring-damper mechanical system are employed to illustrate the usefulness and effectiveness of the proposed method.