On design of stable and robust fuzzy observer-controller for uncertain nonlinear systems based on a grid-point approach

This paper presents the stability and robustness analyses, and design of fuzzy observer-controllers for uncertain multivariable nonlinear systems of which the system states are inaccessible. To proceed with the analysis, the uncertain system is represented by a fuzzy model with uncertain parameters, Based on this model, under a single-grid point (SGP) approach, a fuzzy observer-controller is designed to estimate the system states and to close the feedback loop. A simple stability criterion is derived by estimating some norms 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 observer-controller for nonlinear systems subjected to large parameter uncertainties is developed based on the analysis results of the SGP approach.