Linear matrix inequalities for full and reduced order anti-windup synthesis

This work considers the design of fixed-order antiwindup compensators guaranteeing stability and a given level of L2 performance. The main results show how the design of such a compensator can be cast as a nonconvex optimization problem. It is demonstrated how, under given conditions, this optimization problem can be reduced to a standard LMI (linear matrix inequality) feasibility problem, and situations in which these compensators coincide with those in the literature are described. Moreover, given this formulation, an algorithm for the construction of anti-windup compensators which meet an optimal C2 performance bound is proposed. Furthermore, a lower bound on the C2 performance achievable is shown to be precisely the greater of that predicted by the bounded real lemmas for the linear open-loop plant and for the linear unsaturated closed-loop system.