Dynamic Non-rational Anti-windup for Time-delay Systems with Saturating Inputs

This paper addresses the design of dynamic anti-windup compensators for time-delay systems under amplitude control constraints. Considering that the system is subject to the action of L2 bounded disturbances, a method for computing a non-rational dynamic anti-windup compensator in order to guarantee both that the trajectories of the system are bounded and a certain L2 performance level is achieved by the regulated outputs, is proposed. Based on Lyapunov-Krazovskii functionals, the use of a modified sector condition, and a classical change of variables, sufficient LMI conditions, both in local as well as global contexts, are derived to ensure the input-to-state and the internal stability of the closed-loop system. From these conditions, LMI-based optimization problems are proposed in order to minimize the L2 gain, or in order to maximize the bound on the admissible disturbances for which the trajectories are bounded. The results apply to both stable and unstable open-loop systems and, in particular, for systems presenting delayed states.