Finite-time stability properties of Lur'e systems with piecewise continuous nonlinearities
Systems and Control
2023-02-03 v1 Systems and Control
Dynamical Systems
Abstract
We analyze the stability properties of Lur'e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur'e-Postnikov Lyapunov functions. We first extend an existing result of the literature to establish the global asymptotic stability of the origin under a more general sector condition. We then present the main results of this work, namely additional conditions under which output and state finite-time stability properties also hold for the considered class of systems. We highlight the relevance of these results by certifying the stability properties of two engineering systems of known interest: mechanical systems affected by friction and cellular neural networks.
Cite
@article{arxiv.2302.01175,
title = {Finite-time stability properties of Lur'e systems with piecewise continuous nonlinearities},
author = {Simone Mariano and Romain Postoyan and Luca Zaccarian},
journal= {arXiv preprint arXiv:2302.01175},
year = {2023}
}