Anti-windup Design for Time-delay Systems Subject to Input Saturation An LMI-based Approach

This paper focuses on the study and the characterization of stability regions for linear systems with delayed states and subject to input saturation through anti-windup strategies. In particular, the synthesis of anti-windup gains in order to guarantee the stability of the closedloop system for a region of admissible initial states as large as possible is addressed. Based on the modeling of the closed-loop system, resulting from the controller plus the anti-windup loop, as a linear time-delay system with a deadzone nonlinearity, stability conditions in an LMI form are stated, for both the delay independent and delay dependent contexts, by using quadratic functionals and a modified sector condition. LMI-based optimization schemes for computing the anti-windup gains that lead to the maximization of the size of the region of stability associated to the closed-loop system are then proposed. The application of the technique and the trade-off between the size of the delay and the region of stability are illustrated by means of numerical examples.