Robust fuzzy control of nonlinear discrete-time systems with polytopic uncertainties

This paper deals with the problem of robust fuzzy control for uncertain discrete time nonlinear systems with polytopic uncertainties. Takagi-Sugeno fuzzy models with uncertainties are used in order to model the uncertain nonlinear systems. Parallel distributed compensation is utilized for the construction of the fuzzy controller. A quadratic Lyapunov function is used in order to ensure the robust stability of the T-S fuzzy uncertain system. Finally, the feasibility of some LMI optimization problem provides the desired feedback controller. The effectiveness of the proposed fuzzy controller design is illustrated by applying the proposed approach to a nonlinear uncertain discrete-time system.