Abstract
In this chapter, the problem of fault detection filtering is settled for the nonlinear switched stochastic system in the form of T-S fuzzy model. The objective is to establish a robust fault detection approach for a nonlinear switched system with Brownian motion. Based on the observer-based fuzzy filter as a residual generator, the fault detection problem can be reformulated as a fuzzy filtering problem. By using the piecewise Lyapunov functions and ADT approach, a fuzzy-rule-dependent fault detection filter is established to ensure that the overall dynamic system is mean-square exponential stable and exhibits weighted \(\mathcal {H}_{\infty }\) performance. Moreover, the solvable conditions of the fuzzy filter are established through linearization.
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