Computation of Lyapunov measure for almost everywhere stability

Umesh Vaidya, Prashant G. Mehta

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

Abstract

In our recent paper [1], Lyapunov measure is introduced as a new tool for verifying almost everywhere stability of an invariant set in a nonlinear dynamical system or continuous mapping. It is shown that for almost everywhere stable system explicit formula for the Lyapunov measure can be obtained as a infinite series or as a resolvent of stochastic linear operator. This paper focus on the computation aspects of the Lyapunov measure. Methods for computing these Lyapunov measures are presented based upon set-oriented numerical approaches, which are used for the finite dimensional approximation of the linear operator. Stability results for the finite dimensional approximation of the linear operator are presented. The stability in finite dimensional space results in further weaker notion of stability which in this paper is referred to as coarse stability.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5228-5233
Number of pages6
ISBN (Print)1424401712, 9781424401710
DOIs
StatePublished - Jan 1 2006
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: Dec 13 2006Dec 15 2006

Publication series

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

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
Country/TerritoryUnited States
CitySan Diego, CA
Period12/13/0612/15/06

ASJC Scopus subject areas

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

Fingerprint

Dive into the research topics of 'Computation of Lyapunov measure for almost everywhere stability'. Together they form a unique fingerprint.

Cite this