Modified anti-windup compensators for stable linear systems

In this paper, we use the Small Gain Theorem to study the stability, and develop appropriate convex L₂ gain LMIs for synthesis, of static anti-windup gains. The main contribution of this paper is investigating the effects of delaying the activation of anti-windup by allowing actuators to remain in the saturated regime longer, on their own. The basic idea is to apply anti-windup when the performance of saturated system faces substantial degradation. For this, we present a modified anti-windup scheme along with the appropriate convex LMIs to obtain the gains. For two well-known examples, we show that the modified anti-windup scheme renders better performance than the case of immediate application of anti-windup.