Convex framework for the design of dynamic anti-windup for state-delayed systems

This work addresses the design of dynamic anti-windup compensators for state-delayed systems subject to saturating actuators. Based on the use of a Lyapunov-Krasovskii approach, a generalised sector condition and some congruence transformations, an unified linear matrix inequality-based framework for the synthesis of both rational and non-rational dynamic anti-windup compensators is proposed. Theoretical results to ensure the asymptotic and the input-to-state stabilities of the closed-loop system are presented both in local as well as global contexts. The proposed conditions are cast in convex optimisation problems to compute anti-windup compensators aiming at maximising the bound on the admissible L₂ disturbances, maximising the L₂-gain from the disturbance to the regulated output or maximising the region of attraction of the closed-loop system. Numerical examples illustrate the application of the methodology.