Spatial decay analysis in interconnected dynamical systems using vector Lyapunov functions

Frederik Deroo; Sandra Hirche; Brian Anderson

doi:10.1109/CDC.2014.7039958

Spatial decay analysis in interconnected dynamical systems using vector Lyapunov functions

Frederik Deroo, Sandra Hirche, Brian Anderson

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

Abstract

In this paper we analyze the propagation of input signals in a large-scale network of dynamical systems. Using vector Lyapunov functions, the individual multidimensional subsystems are first reduced to an approximating scalar representation in the form of the evolution of their weighted norm. The norm simultaneously qualifies as a local Lyapunov function for the isolated subsystem. Employing properties of M-matrices, we then derive linear system dynamics which provide an upper bound for the evolution of the original system, and use them to investigate the decay between hops from subsystem to subsystem of the steady state magnitude. Two input signals are considered: Constant input, and a sinusoidal input. The results are demonstrated using numerical simulations.

Original language	English
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Place of Publication	Piscataway, New Jersey, US
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3654-3660
Number of pages	7
Edition	Peer Reviewed
ISBN (Electronic)	9781479977468
ISBN (Print)	9781479977451
DOIs	https://doi.org/10.1109/CDC.2014.7039958 https://doi.org/10.1109/CDC.2014.7039958
Publication status	Published - 2014
Event	53rd IEEE Conference on Decision and Control - Los Angeles, USA, United States Duration: 1 Jan 2014 → …

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	53rd IEEE Conference on Decision and Control
Country/Territory	United States
Period	1/01/14 → …
Other	December 15-17 2014

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Deroo, F., Hirche, S., & Anderson, B. (2014). Spatial decay analysis in interconnected dynamical systems using vector Lyapunov functions. In 53rd IEEE Conference on Decision and Control,CDC 2014 (Peer Reviewed ed., pp. 3654-3660). Article 7039958 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7039958, https://doi.org/10.1109/CDC.2014.7039958

Deroo, Frederik ; Hirche, Sandra ; Anderson, Brian. / Spatial decay analysis in interconnected dynamical systems using vector Lyapunov functions. 53rd IEEE Conference on Decision and Control,CDC 2014. Peer Reviewed. ed. Piscataway, New Jersey, US : Institute of Electrical and Electronics Engineers Inc., 2014. pp. 3654-3660 (Proceedings of the IEEE Conference on Decision and Control; February).

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abstract = "In this paper we analyze the propagation of input signals in a large-scale network of dynamical systems. Using vector Lyapunov functions, the individual multidimensional subsystems are first reduced to an approximating scalar representation in the form of the evolution of their weighted norm. The norm simultaneously qualifies as a local Lyapunov function for the isolated subsystem. Employing properties of M-matrices, we then derive linear system dynamics which provide an upper bound for the evolution of the original system, and use them to investigate the decay between hops from subsystem to subsystem of the steady state magnitude. Two input signals are considered: Constant input, and a sinusoidal input. The results are demonstrated using numerical simulations.",

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series = "Proceedings of the IEEE Conference on Decision and Control",

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Deroo, F, Hirche, S & Anderson, B 2014, Spatial decay analysis in interconnected dynamical systems using vector Lyapunov functions. in 53rd IEEE Conference on Decision and Control,CDC 2014. Peer Reviewed edn, 7039958, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., Piscataway, New Jersey, US, pp. 3654-3660, 53rd IEEE Conference on Decision and Control, United States, 1/01/14. https://doi.org/10.1109/CDC.2014.7039958, https://doi.org/10.1109/CDC.2014.7039958

Spatial decay analysis in interconnected dynamical systems using vector Lyapunov functions. / Deroo, Frederik; Hirche, Sandra; Anderson, Brian.
53rd IEEE Conference on Decision and Control,CDC 2014. Peer Reviewed. ed. Piscataway, New Jersey, US: Institute of Electrical and Electronics Engineers Inc., 2014. p. 3654-3660 7039958 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

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

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AB - In this paper we analyze the propagation of input signals in a large-scale network of dynamical systems. Using vector Lyapunov functions, the individual multidimensional subsystems are first reduced to an approximating scalar representation in the form of the evolution of their weighted norm. The norm simultaneously qualifies as a local Lyapunov function for the isolated subsystem. Employing properties of M-matrices, we then derive linear system dynamics which provide an upper bound for the evolution of the original system, and use them to investigate the decay between hops from subsystem to subsystem of the steady state magnitude. Two input signals are considered: Constant input, and a sinusoidal input. The results are demonstrated using numerical simulations.

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Deroo F, Hirche S, Anderson B. Spatial decay analysis in interconnected dynamical systems using vector Lyapunov functions. In 53rd IEEE Conference on Decision and Control,CDC 2014. Peer Reviewed ed. Piscataway, New Jersey, US: Institute of Electrical and Electronics Engineers Inc. 2014. p. 3654-3660. 7039958. (Proceedings of the IEEE Conference on Decision and Control; February). doi: 10.1109/CDC.2014.7039958, 10.1109/CDC.2014.7039958

Spatial decay analysis in interconnected dynamical systems using vector Lyapunov functions

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