Anti-windup for linear systems with sensor saturation: sufficient conditions for global stability and L2 gain

Abstract

This paper addresses the problem of sensor saturation, in otherwise linear systems, by using an anti-windup like design strategy. The focus is on obtaining sufficient conditions which guarantee global stability and L2 gain. It transpires that the sufficient conditions obtained, which are expressed as linear matrix inequalities (LMI's), take the form of the nominal closed-loop bounded real lemma, and two other bounded real inequalities based on the open-loop characteristics of the plant and the controller. These bounded real inequalities are solvable if the closed-loop linear system (without saturation) is stable, the open-loop linear system is stable and there exists a something akin to a common Lyapunov function between the open and closed-loop systems. These results differ to those obtained in the literature hitherto.