Positivity of Kernel functions for systems with communication delay

Matthew M. Peet, Antonis Papachristodoulou

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

2 Scopus citations

Abstract

The purpose of this paper is to provide further results on a method of constructing Lyapunov functionals for infinite-dimensional systems using semidefinite programming. Specifically, we give a necessary and sufficient condition for positivity of a positive integral operator described by a polynomial kernel. We then show how to combine this result with multiplier operators in order to obtain positive composite Lyapunov functionals. These types of functionals are used to prove stability of linear time-delay systems.

Original languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages2815-2820
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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  • Cite this

    Peet, M. M., & Papachristodoulou, A. (2007). Positivity of Kernel functions for systems with communication delay. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 2815-2820). [4434664] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2007.4434664