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

This note proposes static anti-windup gains design for closed-loop linear systems with saturating inputs providing maximized non-ellipsoidal estimates of the basin of attraction. The proposed design uses sign-indefinite quadratic forms leading to locally positive definite nonquadratic Lyapunov functions. An iterative algorithm that solves the bilinear matrix conditions inherent to this problem is proposed, based on a convex-concave decomposition. A numerical application is presented to illustrate the effectiveness of the proposed method.