$H_{infty}$ Filtering for Fuzzy Singularly Perturbed Systems

This paper considers the problem of designing $H_{infty}$ filters for fuzzy singularly perturbed systems with the consideration of improving the bound of singular-perturbation parameter $epsilon$. First, a linear-matrix-inequality (LMI)-based approach is presented for simultaneously designing the bound of the singularly perturbed parameter $epsilon$, and $H_{infty}$ filters for a fuzzy singularly perturbed system. When the bound of singularly perturbed parameter $epsilon$ is not under consideration, the result reduces to an LMI-based design method for $H_{infty}$ filtering of fuzzy singularly perturbed systems. Furthermore, a method is given for evaluating the upper bound of singularly perturbed parameter subject to the constraint that the considered system is to be with a prescribed $H_{infty}$ performance bound, and the upper bound can be obtained by solving a generalized eigenvalue problem. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.