This brief is concerned with theH∞filtering problem for a class of discrete-time fuzzy systems. The objective is to find a new way to design a stable filter guaranteeing the asymptotic stability and a prescribedH∞performance of the filtering error system. By using the fuzzy Lyapunov function approach and adding slack matrix variables, a new condition forH∞performance analysis is proposed. Then, a linear matrix inequality (LMI)-based approach is developed for designing the fuzzyH∞filter, which can be obtained from the solution of convex optimization problems. When these LMIs are feasible, an explicit expression of a desiredH∞fuzzy filter is given. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.
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Zhang et al. (2009) studied this question.