>tex<$cal H_infty$>/tex<Fuzzy Control Design for Nonlinear Singularly Perturbed Systems With Pole Placement Constraints: An LMI Approach

Abstract

This paper considers the problem of designing an H infinity 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 infinity 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, epsilon. 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 non-linear systems. A numerical example is provided to illustrate the design developed in this paper.

control for fuzzy singularly perturbed systems

“…Very recently, there has appeared some researches on control of fuzzy singularly perturbed systems [2,20,22], but no static output feedback control was investigated in those literatures.…”

Multiobjective tracking control design of T–S fuzzy systems: Fuzzy Pareto optimal approach

“…An effective matrix decoupling technique was developed to derive a single-step LMI condition for the observer-based H ∞ control design [18]. In [19][20][21][22][23], the H ∞ fuzzy control was studied for many different systems to achieve the H ∞ control performance. Recently, the mixed H 2 /H ∞ tracking designs [24][25][26][27][28][29][30] were proposed to minimize the H 2 tracking error with the consideration of a prescribed H ∞ attenuation level to eliminate the influence of uncertain disturbances.…”

The direct adaptive control based on the singularly perturbed model with the unknown consequence parameters

“…A series of analytical results concerning the closed stability properties are achieved by LMI and Lyapunov approach. Assawinchaichote's work [11] is different from those of Liu and Sun's [8][9][10]. Assawinchaichote designed a H ∞ fuzzy controller.…”