Guaranteed cost LMI-based fuzzy controller design for discrete-time nonlinear systems with polytopic uncertainties

This paper focuses on the problem of fuzzy guaranteed cost control and stabilization of discrete-time nonlinear systems with polytopic uncertainties. Takagi-Sugeno fuzzy models with uncertainties are used in order to model the uncertain nonlinear systems and the Parallel Distributed Compensation (PDC) scheme is utilized for the construction of the fuzzy controller. A quadratic cost function is considered as the performance index of the nonlinear system and a quadratic Lyapunov function is used in order to ensure the robust stability of the T-S fuzzy uncertain system. The feasibility of some LMIs provides the state feedback controller which ensures the system´s stability and an upper bound of a quadratic cost function which is minimized. The effectiveness of the proposed fuzzy controller design is illustrated by applying the proposed approach to an uncertain discrete-time chaotic system.