LMI parametrization of Lyapunov functions for infinite-dimensional systems: A framework

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

14 Scopus citations

Abstract

In this paper, we present an algorithmic approach to the construction of Lyapunov functions for infinite-dimensional systems. This paper unifies and significantly extends many previous results which have appeared in conference and journal format. The unifying principle is that any linear parametrization of operators in Hilbert space can be used to construct an LMI parametrization of positive operators via squared representations. For linear systems, we get positive linear operators and hence quadratic Lyapunov functions. For nonlinear systems, we get nonlinear operators and hence non-quadratic Lyapunov functions. Special cases of these results include positive operators defined by multipliers and kernels which are: polynomial; piecewise-polynomial; or semi-separable and apply to systems with delay; multiple spatial domains; or mixed boundary conditions. We also introduce a set of efficient software tools for creating these functionals. Finally, we illustrate the approach with numerical examples.

Original languageEnglish (US)
Title of host publication2014 American Control Conference, ACC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages359-366
Number of pages8
ISBN (Print)9781479932726
DOIs
StatePublished - Jan 1 2014
Event2014 American Control Conference, ACC 2014 - Portland, OR, United States
Duration: Jun 4 2014Jun 6 2014

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2014 American Control Conference, ACC 2014
CountryUnited States
CityPortland, OR
Period6/4/146/6/14

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Keywords

  • Delay systems
  • Distributed parameter systems
  • LMIs

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Peet, M. (2014). LMI parametrization of Lyapunov functions for infinite-dimensional systems: A framework. In 2014 American Control Conference, ACC 2014 (pp. 359-366). [6859228] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2014.6859228