On higher order derivatives of Lyapunov functions

Amir Ali Ahmadi, Pablo A. Parrilo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Scopus citations


This note is concerned with a class of differential inequalities in the literature that involve higher order derivatives of Lyapunov functions and have been proposed to infer asymptotic stability of a dynamical system without requiring the first derivative of the Lyapunov function to be negative definite. We show that whenever a Lyapunov function satisfies these conditions, we can explicitly construct another (standard) Lyapunov function that is positive definite and has a negative definite first derivative. Our observation shows that a search for a standard Lyapunov function parameterized by higher order derivatives of the vector field is less conservative than the previously proposed conditions. Moreover, unlike the previous inequalities, the new inequality can be checked with a convex program. This is illustrated with an example where sum of squares optimization is used.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 American Control Conference, ACC 2011
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages2
ISBN (Print)9781457700804
StatePublished - 2011
Externally publishedYes

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


Dive into the research topics of 'On higher order derivatives of Lyapunov functions'. Together they form a unique fingerprint.

Cite this