@inproceedings{5a05d912ccfe48a58796af557f276323,
title = "Almost global stability results for a class of singularly perturbed systems",
abstract = "We consider a classical singularly perturbed system consisting of a slow subsystem with state x and a fast subsystem with state z, where the small parameter ε multiplies the derivative of z. We assume that the fast system is almost globally asymptotically stable (aGAS) for each fixed x, and the slow system, with z replaced by its equilibrium value, is globally asymptotically stable. We show that there exists a sufficiently small ε∗ > 0 such that the equilibrium point of the overall system is aGAS for all ε ∈ (0, ε∗). We use the theory of density functions as developed by A. Rantzer, D. Angeli and R. Rajaram.",
keywords = "almost global stability, density functions, nonlinear systems, singular perturbations",
author = "Pietro Lorenzetti and George Weiss",
note = "Publisher Copyright: Copyright {\textcopyright} 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/); 22nd IFAC World Congress ; Conference date: 09-07-2023 Through 14-07-2023",
year = "2023",
month = jul,
day = "1",
doi = "10.1016/j.ifacol.2023.10.1665",
language = "אנגלית",
series = "IFAC-PapersOnLine",
publisher = "Elsevier B.V.",
number = "2",
pages = "809--814",
editor = "Hideaki Ishii and Yoshio Ebihara and Jun-ichi Imura and Masaki Yamakita",
booktitle = "IFAC-PapersOnLine",
edition = "2",
}