Improving the stability region of saturated linear systems controlled by dynamic delayed output feedback through anti-windup strategy

Abstract

This paper addresses the problem of determination of stability regions, in fact regions of admissible initial state, as large as possible, for linear systems with delayed outputs and subject to input saturation and bounded controlled outputs, through anti-windup strategies. The closed-loop system resulting from the open-loop system with delayed output, the dynamic output controller plus the anti-windup loop is modelled as a linear time-delay system with a dead-zone nonlinearity. Constructive delay-dependent stability condition is then formulated by using a quadratic Lyapunov-Krasovskii functional. The optimization problem for computing the anti-windup gain that maximizes the size of the associated region of stability is directly expressed as the optimization of a convex criterion under LMI constraints.