Fuzzy-Modeled Prescribed Performance Integral Controller Design for Nonlinear Descriptor System With Uncertainties

Abstract

A suitable solution for a nonlinear descriptor system with uncertainties is considered in this paper by designing a fuzzy-modeled prescribed performance integral controller. The system with a parasitic parameter ε is known as the descriptor system, and this parasitic parameter is used for specifying a fast mode of such a system. Based on a linear matrix inequality (LMI) approach, the interaction of fast and slow dynamic modes which causes ill-conditioned LMI result has normally occurred in the nonlinear descriptor system with uncertainties. Therefore, with the design of the fuzzy-modeled prescribed performance integral controller, such a system with parametric uncertainties is represented by a Takagi-Sugeno fuzzy model, and the H ∞ fuzzy state-feedback controller is designed to achieve an adequate condition for overcoming the effects of the parasitic parameter, the uncertainties, and the exogenous input disturbance. Moreover, the integral controller is added to increase the performances of stability. In summary, the design process of the proposed controller and the numerical example serve to illustrate various performance results of the proposed controller. INDEX TERMS H ∞ fuzzy controller, integral controller, linear matrix inequality (LMI), Takagi-Sugeno fuzzy model, uncertain nonlinear descriptor system.