Nonquadratic global asymptotic stability certificates for saturated linear feedbacks
Abstract
We establish sufficient conditions for positive (semi-)definiteness, with or without radial unboundedness, for nonquadratic Lyapunov function constructed as sign-indefinite quadratic forms involving the state and the deadzone of a suitable input. We then use these conditions to build weak nonquadratic Lyapunov functions establishing global asymptotic stability of linear systems in feedback through a saturation, leveraging invariance principles. Our results are shown to be non-conservative (necessary and sufficient) for a family of well known prototypical examples of linear SISO feedbacks that are not globally exponentially stabilizable (the so-called ANCBI plants). Our multi-input extension leads to convex stability analysis tests, formulated as linear matrix inequalities that are applicable to ANCBI non-globally-exponentially-stabilizable plants.
Cite
@article{arxiv.2601.07431,
title = {Nonquadratic global asymptotic stability certificates for saturated linear feedbacks},
author = {Andrea Cristofaro and Luca Zaccarian},
journal= {arXiv preprint arXiv:2601.07431},
year = {2026}
}