Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization

We present a method for the synthesis of a control law for input constrained linear systems that incorporates both a traditional linear output-feedback controller as well as a static anti-windup compensator. Unlike traditional two-step anti-windup controller designs in which the linear controller and anti-windup compensator are designed sequentially, our method synthesizes all controller parameters simultaneously. This one-step design retains the anti-windup structure, thus providing structurally 'a priori' compensation for saturation. We derive sufficient conditions for guaranteeing global quadratic stability and for satisfying multiple, possibly conflicting, performance objectives on the constrained and unconstrained closed-loop dynamics. The resulting synthesis problem is recast as an optimization over linear matrix inequalities (LMIs). We demonstrate the proposed method on a benchmark problem.