Synthesis of a static anti‐windup compensator via linear matrix inequalities

Abstract

Abstract In this paper, we propose a design method of a static anti‐windup compensator that guarantees robust stability subject to input saturation and suppresses the degradation of robust performance during the saturation period. In previous studies, this problem has been considered to be equivalent to a static output feedback design problem, which is essentially a non‐convex problem. We show that this problem can be reduced to an equivalent convex problem by using an appropriate sector transformation. The numerical solution can be obtained efficiently by solving linear matrix inequalities (LMIs). Further, a constant scaling matrix is introduced to the condition in order to reduce the conservativeness. In this case, since the design problem is no more LMIs, an algorithm for solving the problem by LMI iterations is presented. Four numerical examples are given to illustrate the effectiveness of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.