Design of stable and robust fuzzy controllers for uncertain multivariable nonlinear systems

Abstract—This paper presents the stability and robustness analysis for multivariable fuzzy control systems subject to parameter uncertainties based on a single-grid-point (SGP) approach. To perform the analysis, we represent a multivariable nonlinear system using a TS-fuzzy plant model. Three design approaches of fuzzy controllers are introduced to close the feedback loop. By estimating the matrix measures of the system parame-ters and parameter uncertainties, stability and robustness conditions for different cases are derived. Application examples will be given to show the design procedures and the merits of the proposed fuzzy controller. Index Terms—fuzzy control, nonlinear system robustness, parameter un-certainty, stability. I