The L2 anti-winup problem: Its definition and solution

The problems of ‘windup’ (linear closed-loop systems not behaving as they should due to input saturation) and synthesizing ‘anti-windup’ compensator modifications have been studied for a long time. Unfortunately, the anti-windup problem has never been adequately formalized mathematically and almost all existing solutions are heuristic in nature. In this work, we formalize the goal of anti-windup synthesis in a natural way and we provide an algorithm that achieves this goal. We demonstrate our algorithm's robustness properties and its relationship to optimal anti-windup. A simple numerical example is provided to illustrate our technique.