Fuzzy output regulator design of discrete affine systems with multiple time-varying delays

This paper presents a Takagi–Sugeno (T–S) fuzzy model-based regulator for a class of discrete affine nonlinear systems with multiple time-varying delays. First, combining the T–S fuzzy representation and Lyapunov–Krasovskii method, we derive the sufficient conditions for the unforced affine system with multiple time-varying delays, disturbances, and non-vanishing bias at the origin. These stability conditions are not derived in current literature. Next, the fuzzy output regulator is proposed by introducing a memoryless fuzzy observer and a fuzzy integral compensator. Then, asymptotic output regulation and state estimation is achieved by solving linear matrix inequalities (LMIs) in a two-step manner. Moreover, an H∞ performance criterion is guaranteed for disturbance attenuation. Compared to traditional approaches, this paper does not require exact information of partial states, each time-varying delay, and the desired operational point. The proposed controller yields a multi-task regulation without needing controller redesign once the output command is changed. Finally, numerical simulations are carried out on two intuitive time-delay systems to illustrate the expected performance.