H∞ filtering for fuzzy singularly perturbed systems with pole placement constraints: an LMI approach

This paper addresses the problem of designing an H_∞ filter for a class of nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a fuzzy H_∞ controller that guarantees that i) the L₂-gain from an exogenous input to a filter error is less than or equal to a prescribed value and ii) the poles of each local filter are within a prespecified region. In order to alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities, which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones, and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.