Stability and robustness analysis of uncertain multivariable continuous-time nonlinear systems with digital fuzzy controller

Abstract

This paper presents the analyses of the stability and robustness of multivariable continuous-time nonlinear systems subject to parameter uncertainties and with digital fuzzy controllers. To proceed with the analysis, first, an uncertain multivariable nonlinear plant will be represented by a fuzzy plant model with parameter uncertainties. Second, a digital fuzzy controller is designed to close the feedback loop. Third, the stability criteria, the robust area and the largest sampling period will be derived in terms of the matrix measures of the system parameters and the norms of the parameter uncertainties. An application example on stabilizing an uncertain nonlinear mass-spring-damper system will be given to show the stabilizability and robustness properties of the proposed digital fuzzy controller.