On infinity norms as Lyapunov functions for continuous-time dynamical systems

Mircea Lazar, Alina I. Doban

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

8 Citations (Scopus)

Abstract

This paper considers the synthesis of polyhedral Lyapunov functions for continuous-time dynamical systems. A proper conic partition of the state-space is employed to construct a finite set of linear inequalities in the elements of the Lyapunov weight matrix. For dynamics described by linear and polytopic differential inclusions, it is proven that the feasibility of the derived set of linear inequalities is necessary and sufficient for the existence of an infinity norm Lyapunov function. Furthermore, it is shown that the developed solution naturally applies to relevant classes of continuous-time nonlinear systems. An extension to non-symmetric polyhedral Lyapunov functions is also presented.

Original languageEnglish
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages7567-7572
Number of pages6
ISBN (Print)9781612848006
DOIs
Publication statusPublished - 1 Dec 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Hilton Orlando Bonnet Creek, Orlando, FL, United States
Duration: 12 Dec 201115 Dec 2011
Conference number: 50
http://www.ieeecss.org/CAB/conferences/cdcecc2011/

Conference

Conference2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Abbreviated titleCDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1115/12/11
Internet address

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  • Cite this

    Lazar, M., & Doban, A. I. (2011). On infinity norms as Lyapunov functions for continuous-time dynamical systems. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 7567-7572). [6161163] Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2011.6161163