Constructive design of output feedback weakened anti-windup compensators for linear systems with additive/multiplicative perturbations

A two-step algorithm for the synthesis of output feedback weakened anti-windup compensators is proposed for the case of additively perturbed systems. The first step determines a state feedback stabilizer guaranteeing a finite gain on a suitable nonlinear “mismatch” system. In the second step, a loop-shaping approach is adopted to design a linear filter which ensures overall robust stability, meanwhile minimizing the amount of anti-windup performance sacrificed. Both steps can be efficiently implemented using standard LMI software.