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

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 L-2 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.