@inproceedings{903e81b7ad114fca8835287c03d43e66,
title = "Higher Order Derivatives of Lyapunov Functions for Stability of Systems with Inputs",
abstract = "In this paper we study an alternative method for determining stability of dynamical systems by inspecting higher order derivatives of a Lyapunov function. The system can be time invariant or time varying; in both cases we define the higher order derivatives when there are inputs. We then claim and prove that if there exists a linear combination of those higher order derivatives with non-negative coefficients (except that the coefficient of the 0-th order term needs to be positive) which is negative semi-definite, then the system is globally uniformly asymptotically stable. The proof involves repeated applications of comparison principle for first order differential relations. We also show that a system with inputs whose auxiliary system admits a Lyapunov function satisfying the aforementioned conditions is input-to-state stable.",
author = "Shenyu Liu and Daniel Liberzon",
year = "2019",
month = dec,
doi = "10.1109/CDC40024.2019.9029302",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "6146--6151",
booktitle = "2019 IEEE 58th Conference on Decision and Control, CDC 2019",
address = "United States",
note = "58th IEEE Conference on Decision and Control, CDC 2019 ; Conference date: 11-12-2019 Through 13-12-2019",
}