CaltechAUTHORS
  A Caltech Library Service

On a Converse theorem for Finite-time Lyapunov Functions to Estimate Domains of Attraction

Pandey, Ayush and Ames, Aaron D. (2020) On a Converse theorem for Finite-time Lyapunov Functions to Estimate Domains of Attraction. In: 2020 American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 3763-3769. ISBN 9781538682661. https://resolver.caltech.edu/CaltechAUTHORS:20200730-143943387

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20200730-143943387

Abstract

The main result of the paper is a new converse theorem for finite-time Lyapunov functions. We show the existence of a finite-time Lyapunov function for an autonomous continuous-time nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in finite-time Lyapunov function theory by providing an alternative converse proof for the existence of finite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global finite-time Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efficiently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.23919/acc45564.2020.9147709DOIArticle
ORCID:
AuthorORCID
Pandey, Ayush0000-0003-3590-4459
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2020 AACC.
Record Number:CaltechAUTHORS:20200730-143943387
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200730-143943387
Official Citation:A. Pandey and A. D. Ames, "On a Converse theorem for Finite-time Lyapunov Functions to Estimate Domains of Attraction," 2020 American Control Conference (ACC), Denver, CO, USA, 2020, pp. 3763-3769, doi: 10.23919/ACC45564.2020.9147709
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104668
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:31 Jul 2020 14:23
Last Modified:03 Aug 2020 21:00

Repository Staff Only: item control page