Results on linear LMI-based external anti-windup design

We study linear anti-windup augmentation for linear control systems with saturated linear plants in a special case when the anti-windup compensator can only modify the input and output of the windup-prone linear controller. We also measure the arising performance in terms of the finite L₂ gain from selected exogenous inputs to selected performance outputs. Our main results are a system theoretic feasibility characterization for fixed order anti-windup design and a linear matrix inequality (LMI) formulation for optimal static and plant-order anti-windup design. Interpretations of lower bounds on the achievable performance are also given. The effectiveness of the design procedure is demonstrated on a simulation example.