A generalized chain rule and a bound on the continuity of solutions and converse Lyapunov functions

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

1 Scopus citations

Abstract

This paper gives a bound on the continuity of solutions to nonlinear ordinary differential equations. Continuity is measured with respect to an arbitrary Sobolev norm. This result is used to give a bound on the continuity of a common converse Lyapunov function. A major technical contribution of this paper is to give an explicit formula for nth-degree derivatives of the composition of differentiable mappings from ℝn to ℝn. This is a generalization of the formula of Faa di Bruno which dealt with differentiable mappings from ℝ to ℝ. It is expected that continuity bounds of the type given in this paper can be used to prove the existence of bounded-degree polynomial Lyapunov functions or give bounds on the Lyapunov exponent.

Original languageEnglish (US)
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages3155-3161
Number of pages7
DOIs
StatePublished - Dec 1 2009
Externally publishedYes
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: Dec 15 2009Dec 18 2009

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period12/15/0912/18/09

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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    Peet, M. M. (2009). A generalized chain rule and a bound on the continuity of solutions and converse Lyapunov functions. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 3155-3161). [5400414] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5400414