Static Linear Anti-Windup Design With Sign-Indefinite Quadratic Forms

We design static anti-windup gains to mitigate the effect of input saturation in linear output feedback closed loops. The design is conducted with the help of a non-quadratic Lyapunov function involving sign-indefinite quadratic forms, which allows for additional degrees of freedom to be exploited, for the anti-windup gain design. Synthesis conditions, combining the use of sign-indefinite quadratic forms and several sector bound properties are stated in the form of bilinear matrix inequalities ensuring global exponential stability of the closed-loop system. An iterative design algorithm is then devised, based on the resolution of a sequence of semidefinite programs. The superiority of the proposed technique over classical quadratic constructions is illustrated on an example borrowed from the literature, where quadratic positive definite functions are ineffective.