Static anti-windup controller synthesis using simultaneous convex design

By combining results from Mulder et al. (2001) and Scherer et al. (1997), we present a method for the synthesis of a control law which incorporates both a traditional linear output-feedback controller as well as a static anti-windup compensator. Unlike traditional anti-windup control design, in which the linear controller and anti-windup compensator are synthesized sequentially, our method synthesizes all controller parameters simultaneously, thus providing an a priori account of the effect of saturation on the closed-loop dynamics. Moreover, we derive sufficient conditions for quadratic stability and (possibly) multiple performance bounds on the closed-loop dynamics such that the entire synthesis is cast as an optimization problem over linear matrix inequalities (LMIs).