H∞ Control for T–S Fuzzy System via Delayed State Feedback: Application to Two-Link Robotic System

This paper introduces a fuzzy control design method for nonlinear systems with H∞ performance index. First, the Takagi–Sugeno (T–S) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a parallel distributed compensation (PDC) based delayed fuzzy controller is developed. The advantage of the proposed control design is that only a simple fuzzy controller is used in our approach without the feedback linearization technique. By constructing a suitable Lyapunov–Krasovskii functional (LKF) and using the Wirtinger-based inequality method, the proposed fuzzy control problem is designed in terms of linear matrix inequality (LMI) problem. Finally, the simulation result is presented to show the effectiveness of the proposed condition.