Stable and robust fuzzy control for uncertain nonlinear systems based on a grid-point approach

Abstract

This paper presents the stability and robustness analyses of uncertain nonlinear control systems. To proceed with the analysis, the uncertain nonlinear system is represented by a fuzzy model with uncertainties. Based on this model, under a single-grid-point (SGP) approach, a fuzzy controller is designed to close the feedback loop. A simple stability criterion is derived by estimating the norm of the system parameters and the matrix measure, and a robust area in the uncertain parameter space is defined. The design methodology of a multiple-grid-point (MGP) fuzzy controller for nonlinear systems subjected to large parameter uncertainties is developed based on the analysis results of the SGP approach.