H∞ fuzzy control design for nonlinear singularly perturbed systems with pole placement constraints: an LMI approach

This paper considers the problem of designing an H_∞ fuzzy controller with pole placement constraints for a class of nonlinear singularly perturbed systems. Based on a linear matrix inequality (LMI) approach, we develop an H_∞ fuzzy controller that guarantees 1) the L₂-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and 2) the closed-loop poles of each local system to be within a pre-specified LMI stability region. In order to alleviate the ill-conditioned LMIs 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. 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.