H_∞ Control design for discrete‐time nonlinear delayed systems

Abstract

Summary This manuscript concerns the stabilization of discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems with additive time‐varying delay components. By constructing a suitable fuzzy Lyapunov‐Krasovskii functional (LKF) with membership functions, the sufficient condition of the stability criteria has been established for the discrete‐time T‐S fuzzy systems with additive time‐varying delays. To do this, the extended version of Wirtinger's inequality is used to bound the forward differences of the LKF. By utilizing the T‐S fuzzy model approach, the dynamics of each fuzzy rule is expressioned by a linear system. Then, a fuzzy controller is designed to guarantee the H∞$$ {H}_{\infty } $$ performance of the closed‐loop system formulated in terms of linear matrix inequalities (LMIs). Finally, the numerical simulations are carried out to demonstrate the effectiveness and feasibility of our theoretical findings.