Multistage anti-windup design for linear systems with saturation nonlinearity: enlargement of the domain of attraction

This paper considers the multistage anti-windup (AW) design for linear systems with saturation nonlinearity, with the objective of enlarging the domain of attraction of the resulting closed-loop system. We present results for both static and dynamic AW compensation gains, in terms of linear matrix inequalities. Iterative algorithms are established to obtain the AW compensation gains that maximize the estimate of the domain of attraction. In addition, a particle swarm optimization-based systematic method is proposed to determine the design point of the multistage AW scheme and to set the initial conditions of the established iterative algorithms. Using the proposed method, benefits of the multistage AW on the domain of attraction are illustrated through a benchmark example.