Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions

Matthew M. Peet, Antonis Papachristodoulou

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

5 Scopus citations

Abstract

In this paper, we introduce the class of semi-separable kernel functions for use in constructing Lyapunov functions for distributed-parameter systems such as delaydifferential equations. We then consider the subset of semiseparable kernel functions defined by polynomials. We show that the set of such kernels which define positive forms can be parameterized by positive semidefinite matrices. In the particular case of linear time-delay systems, we show how to construct the derivative of Lyapunov functions defined by piecewise continuous semi-separable kernels and give numerical examples which illustrate some advantages over standard polynomial kernel functions.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages847-852
Number of pages6
DOIs
StatePublished - Dec 1 2008
Externally publishedYes
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Publication series

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

Other

Other47th IEEE Conference on Decision and Control, CDC 2008
CountryMexico
CityCancun
Period12/9/0812/11/08

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ASJC Scopus subject areas

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

Cite this

Peet, M. M., & Papachristodoulou, A. (2008). Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 847-852). [4739245] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2008.4739245