@inproceedings{cd37399df9654ff088714c8a5bae8847,
title = "On almost Lyapunov functions",
abstract = "We study asymptotic stability properties of nonlinear systems in the presence of 'almost Lyapunov' functions which decrease along solutions in a given region not everywhere but rather on the complement of a set of small volume. Nothing specific about the structure of this set is assumed besides an upper bound on its volume. We show that solutions starting inside the region approach a small set around the origin whose volume depends on the volume of the set where the Lyapunov function does not decrease, as well as on other system parameters. The result is established by a perturbation argument which compares a given system trajectory with nearby trajectories that lie entirely in the set where the Lyapunov function is known to decrease, and trades off convergence speed of these trajectories against the expansion rate of the distance to them from the given trajectory.",
author = "Daniel Liberzon and Charles Ying and Vadim Zharnitsky",
note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 ; Conference date: 15-12-2014 Through 17-12-2014",
year = "2014",
doi = "10.1109/CDC.2014.7039864",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "February",
pages = "3083--3088",
booktitle = "53rd IEEE Conference on Decision and Control,CDC 2014",
address = "United States",
edition = "February",
}