Connection between almost everywhere stability of an ODE and advection PDE

Rajeev Rajaram, Umesh Vaidya, Makan Fardad

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

7 Scopus citations

Abstract

A result on the necessary and sufficient conditions for almost everywhere stability of an invariant set in continuoustime dynamical systems is presented. It is shown that the existence of a Lyapunov density is equivalent to the almost everywhere stability of an invariant set. Furthermore, such a density can be obtained as the positive solution of a linear partial differential equation analogous to the positive solution of Lyapunov equation for stable linear systems.

Original languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages5880-5885
Number of pages6
DOIs
StatePublished - Dec 1 2007
Externally publishedYes
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

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

Other

Other46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

ASJC Scopus subject areas

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

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