Further results on full-order anti-windup synthesis: exploiting the stability multiplier

Abstract Several approaches to the multivariable anti-windup problem are based on a Lyapunov formulation of the Circle Criterion. Usually these approaches culminate in some form of linear-matrix-inequality (LMJ) feasibility problem, in which the Lyapunov function, the anti-windup compensator state-space matrices and the so-called “stability multiplier” are sought. In general, this is an overparametrised problem, with degrees of freedom available for tuning. Typically, these degrees of freedom are either not used, or they become ’lost’ in the optimisation problem. Here, the full-order anti-windup problem is reconsidered and it is shown how the available degrees of freedom are related to the well-posedness of the closed-loop system. However, it is further shown that full exploitation of the extra degress of freedom is difficult. Ultimately, this leads to the conclusion that an existing form of coprime-factor based anti-windup compensator appears to be ’optimal’.