$k$-Contraction in a Generalized Lurie System
Systems and Control
2025-05-20 v4 Systems and Control
Abstract
We derive a sufficient condition for -contraction in a generalized Lurie system~(GLS), that is, the feedback connection of a nonlinear dynamical system and a memoryless nonlinear function. For , this reduces to a sufficient condition for standard contraction. For , this condition implies that every bounded solution of the GLS converges to an equilibrium, which is not necessarily unique. We demonstrate the theoretical results by analyzing -contraction in a biochemical control circuit with nonlinear dissipation terms.
Cite
@article{arxiv.2309.07514,
title = {$k$-Contraction in a Generalized Lurie System},
author = {Ron Ofir and Jean-Jacques Slotine and Michael Margaliot},
journal= {arXiv preprint arXiv:2309.07514},
year = {2025}
}