Robust Static Output Feedback Fuzzy Control Design for Nonlinear Discrete-Time Systems with Persistent Bounded Disturbances

To date, nonlinear l∞ -gain static output feedback control problems have not been solved by the conventional control methods for nonlinear discrete-time systems with persistent bounded disturbances. This study introduces static output feedback fuzzy control scheme to deal with the nonlinear l∞ -gain control problem. The structure of static output feedback fuzzy control is simpler than that of dynamic output feedback fuzzy control. Based on the Takagi and Sugeno (T-S) fuzzy model, a static output feedback fuzzy controller is developed to minimize the upper bound of l∞ -gain of the closed-loop system under some linear matrix inequality (LMI) constraints. A singular value decomposition (SVD) method is proposed in this study to solve the l∞ -gain static output feedback fuzzy control problem for the nonlinear discrete-time systems in terms of solving an LMI-based minimization problem. The proposed static output feedback fuzzy control scheme can efficiently attenuate the peak of perturbation due to persistent bounded disturbances for the nonlinear discrete-time systems. Simulation examples are given to illustrate the design procedures and to confirm the l∞ -gain performance of the proposed method.