Contractivity Analysis and Control Design for Lur'e Systems: Lipschitz, Incrementally Sector Bounded, and Monotone Nonlinearities
Optimization and Control
2025-04-08 v2
Abstract
In this paper, we study the contractivity of Lur'e dynamical systems whose nonlinearity is either Lipschitz, incrementally sector bounded, or monotone. We consider both the discrete- and continuous-time settings. In each case, we provide state-independent linear matrix inequalities (LMIs) which are necessary and sufficient for contractivity. Additionally, we provide LMIs for the design of controller gains such that the closed-loop system is contracting. Finally, we provide a numerical example for control design.
Cite
@article{arxiv.2503.20177,
title = {Contractivity Analysis and Control Design for Lur'e Systems: Lipschitz, Incrementally Sector Bounded, and Monotone Nonlinearities},
author = {Ryotaro Shima and Alexander Davydov and Francesco Bullo},
journal= {arXiv preprint arXiv:2503.20177},
year = {2025}
}
Comments
Submitted to CDC 2025