Using anti-windup loops for enlarging the stability region of time-delay systems subject to input saturation

This paper focus 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 closed-loop system for a region of admissible initial states as large as possible is addressed. Based on the modelling 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 new 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 a numerical example.