Exponential Convergence of Time‐Delay Systems in the Presence of Bounded Disturbances

In this paper, the problem of control design for exponential convergence of state/input delay systems with bounded disturbances is considered. Based on the Lyapunov–Krasovskii method combining with the delay‐decomposition technique, a new sufficient condition is proposed for the existence of a state feedback controller, which guarantees that all solutions of the closed‐loop system converge exponentially (with a pre‐specified convergence rate) within a ball whose radius is minimized. The obtained condition is given in terms of matrix inequalities with one parameter needing to be tuned, which can be solved by using a one‐dimensional search method with Matlab’s LMI Toolbox to minimize the radius of the ball. Two numerical examples are given to illustrate the superiority of the proposed method.