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

Matthew M. Peet; Antonis Papachristodoulou

doi:10.1109/CDC.2008.4739245

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

Matthew M. Peet, Antonis Papachristodoulou

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	847-852
Number of pages	6
ISBN (Print)	9781424431243
DOIs	https://doi.org/10.1109/CDC.2008.4739245
State	Published - 2008
Externally published	Yes
Event	47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico Duration: Dec 9 2008 → Dec 11 2008

Publication series

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

Other

Other	47th IEEE Conference on Decision and Control, CDC 2008
Country/Territory	Mexico
City	Cancun
Period	12/9/08 → 12/11/08

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2008.4739245

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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). Article 4739245 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2008.4739245

Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions. / Peet, Matthew M.; Papachristodoulou, Antonis.
Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc., 2008. p. 847-852 4739245 (Proceedings of the IEEE Conference on Decision and Control).

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

Peet, MM & 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., 4739245, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 847-852, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 12/9/08. https://doi.org/10.1109/CDC.2008.4739245

Peet MM, Papachristodoulou A. Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc. 2008. p. 847-852. 4739245. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2008.4739245

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AB - 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.

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

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