Design of stable and robust fuzzy controller for uncertain nonlinear systems: Lyapunov´s function approach

This paper presents the analysis of stability and robustness of an uncertain nonlinear fuzzy system. To proceed with the analysis, the uncertain nonlinear plant is represented by a fuzzy model that includes parameter uncertainty information. Then, three design approaches will be introduced to close the feedback loop. By using the Lyapunov´s stability theory, the closed loop uncertain fuzzy control system is shown to be stable if there exists a positive definite solution for an algebraic Riccati equation (ARE) derived. An example on stabilizing an uncertain nonlinear mass-spring-damper system is given to illustrate the stabilizability and robustness properties of the proposed fuzzy controller