Positivity of Kernel functions for systems with communication delay

Matthew M. Peet; Antonis Papachristodoulou

doi:10.1109/CDC.2007.4434664

Positivity of Kernel functions for systems with communication delay

Matthew M. Peet, Antonis Papachristodoulou

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2815-2820
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434664
State	Published - 2007
Externally published	Yes
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 12/14/07

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2007.4434664

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). Article 4434664 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434664

Positivity of Kernel functions for systems with communication delay. / Peet, Matthew M.; Papachristodoulou, Antonis.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 2815-2820 4434664 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Peet, MM & 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., 4434664, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 2815-2820, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434664

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title = "Positivity of Kernel functions for systems with communication delay",

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.",

author = "Peet, {Matthew M.} and Antonis Papachristodoulou",

note = "Funding Information: We thank Mike Hudson, Jim Bartlett, Alain Blanchard, and Jamila Oukbir for comments. The Canadian Time Assignment Committee allocated CFHT observing time. The CFHT organization provided the technical support which made these observations feasible. Funding was provided by NSERC and NRC of Canada.; 46th IEEE Conference on Decision and Control 2007, CDC ; Conference date: 12-12-2007 Through 14-12-2007",

year = "2007",

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AU - Papachristodoulou, Antonis

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N2 - 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.

AB - 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.

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U2 - 10.1109/CDC.2007.4434664

DO - 10.1109/CDC.2007.4434664

M3 - Conference contribution

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SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2815

EP - 2820

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -

Positivity of Kernel functions for systems with communication delay

Abstract

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ASJC Scopus subject areas

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