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The nonfragile H ∞ filtering problem for a kind of Takagi-Sugeno (T-S) fuzzy stochastic system which has a time-varying delay and parameter uncertainties has been studied in this paper. Sufficient conditions for stochastic input-to-state stability (SISS) of the fuzzy stochastic systems are obtained. Attention is focused on the design of a nonfragile H ∞ filter such that the filtering error system can tolerate some level of the gain variations in the filter and the H ∞ performance level also could be satisfied. By using the SISS result, the approach to design the nonfragile filter is proposed in terms of linear matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.

Nonfragile Robust H ∞ Filter Design for a Class of Fuzzy Stochastic Systems with Stochastic Input-to-State Stability