Design of Robust Fuzzy Controllers for Uncertain Nonlinear Systems

This thesis deals with the analysis and design of robust fuzzy controllers for uncertain nonlinear systems using Takagi-Sugeno (T-S) model based approach. A T-S fuzzy model is used here to approximate the uncertain nonlinear systems where the nominal model and uncertain terms of the consequent parts of the fuzzy model are identified by a linear programming approach and then they are expressed in a form suitable for robust fuzzy controller design. With the derived T-S fuzzy model, various types of robust fuzzy controllers are designed that guarantee not only stability but also satisfy the specified performance criteria of the closed-loop control system. The first type of T-S controller is a robust fuzzy guaranteed cost controller for trajectory tracking in uncertain nonlinear systems. The fixed Lyapunov function based approach is used to develop the robust controller and the design conditions are derived as a problem of solving a set of linear matrix inequalities (LMIs). Next, this research work focuses on robust stabilization, robust H∞ stabilization and robust H∞ tracking control of uncertain nonlinear systems by using a richer class of Lyapunov function called parametric Lyapunov function. This parametric Lyapunov function based approach attempts to reduce the conservatism associated in the controller design for nonlinear systems with slowly varying uncertainties. The design conditions are derived as matrix inequality involving parametric uncertainties and then they are reduced to finite dimensional matrix inequalities by using the multiconvexity concept. These matrix inequalities are then solved by an iterative LMI based algorithm. Finally, the results of standard state-space T-S fuzzy system with parametric Lyapunov function based approach are extended to synthesize the robust controller for application to uncertain fuzzy descriptor systems.