Abstract
This paper is concerned with the robust \(H_{\infty }\) filtering problem of nonlinear stochastic delayed systems with Markov jumps, where time delay exists in state equation, measurement equation and controlled output. Firstly, by introducing a nonlinear stochastic bounded real lemma, we present the \(H_{\infty }\) filter design via solving a set of Hamilton-Jacobi inequalities (HJIs). Secondly, by using fuzzy approach, the \(H_{\infty }\) filter can be designed via solving a set of Linear Matrix inequalities instead of HJIs. Finally, two numerical examples are given to show the effectiveness of our results.
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