Global stability for monotone tridiagonal systems with negative feedback

Liming Wang; Patrick De Leenheer; Eduardo D. Sontag

doi:10.1109/CDC.2008.4739063

Global stability for monotone tridiagonal systems with negative feedback

Liming Wang, Patrick De Leenheer, Eduardo D. Sontag

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

2 Scopus citations

Abstract

This paper studies monotone tridiagonal systems with negative feedback. These systems possess the Poincaré-Bendixson property, which implies that, if orbits are bounded, if there is a unique steady state and this unique equilibrium is asymptotically stable, and if one can rule out periodic orbits, then the steady state is globally asymptotically stable. Different approaches are discussed to rule out period orbits. One is based on direct linearization, while the other uses the theory of second additive compound matrices. Among the examples that will illustrate our main theoretical results is the classical Goldbeter model of the circadian rhythm.

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	4091-4096
Number of pages	6
ISBN (Print)	9781424431243
DOIs	https://doi.org/10.1109/CDC.2008.4739063
State	Published - 2008
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

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2008.4739063

Cite this

Wang, L., Leenheer, P. D., & Sontag, E. D. (2008). Global stability for monotone tridiagonal systems with negative feedback. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 4091-4096). Article 4739063 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2008.4739063

@inproceedings{c0340cd54a1a4150bc480f203652ac44,

title = "Global stability for monotone tridiagonal systems with negative feedback",

abstract = "This paper studies monotone tridiagonal systems with negative feedback. These systems possess the Poincar{\'e}-Bendixson property, which implies that, if orbits are bounded, if there is a unique steady state and this unique equilibrium is asymptotically stable, and if one can rule out periodic orbits, then the steady state is globally asymptotically stable. Different approaches are discussed to rule out period orbits. One is based on direct linearization, while the other uses the theory of second additive compound matrices. Among the examples that will illustrate our main theoretical results is the classical Goldbeter model of the circadian rhythm.",

author = "Liming Wang and Leenheer, {Patrick De} and Sontag, {Eduardo D.}",

year = "2008",

doi = "10.1109/CDC.2008.4739063",

language = "English (US)",

isbn = "9781424431243",

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

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4091--4096",

booktitle = "Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008",

address = "United States",

note = "47th IEEE Conference on Decision and Control, CDC 2008 ; Conference date: 09-12-2008 Through 11-12-2008",

}

Wang, L, Leenheer, PD & Sontag, ED 2008, Global stability for monotone tridiagonal systems with negative feedback. in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008., 4739063, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4091-4096, 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 12/9/08. https://doi.org/10.1109/CDC.2008.4739063

Global stability for monotone tridiagonal systems with negative feedback. / Wang, Liming; Leenheer, Patrick De; Sontag, Eduardo D.
Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. Institute of Electrical and Electronics Engineers Inc., 2008. p. 4091-4096 4739063 (Proceedings of the IEEE Conference on Decision and Control).

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

TY - GEN

T1 - Global stability for monotone tridiagonal systems with negative feedback

AU - Wang, Liming

AU - Leenheer, Patrick De

AU - Sontag, Eduardo D.

PY - 2008

Y1 - 2008

N2 - This paper studies monotone tridiagonal systems with negative feedback. These systems possess the Poincaré-Bendixson property, which implies that, if orbits are bounded, if there is a unique steady state and this unique equilibrium is asymptotically stable, and if one can rule out periodic orbits, then the steady state is globally asymptotically stable. Different approaches are discussed to rule out period orbits. One is based on direct linearization, while the other uses the theory of second additive compound matrices. Among the examples that will illustrate our main theoretical results is the classical Goldbeter model of the circadian rhythm.

AB - This paper studies monotone tridiagonal systems with negative feedback. These systems possess the Poincaré-Bendixson property, which implies that, if orbits are bounded, if there is a unique steady state and this unique equilibrium is asymptotically stable, and if one can rule out periodic orbits, then the steady state is globally asymptotically stable. Different approaches are discussed to rule out period orbits. One is based on direct linearization, while the other uses the theory of second additive compound matrices. Among the examples that will illustrate our main theoretical results is the classical Goldbeter model of the circadian rhythm.

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DO - 10.1109/CDC.2008.4739063

M3 - Conference contribution

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SN - 9781424431243

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4091

EP - 4096

BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 47th IEEE Conference on Decision and Control, CDC 2008

Y2 - 9 December 2008 through 11 December 2008

ER -

Global stability for monotone tridiagonal systems with negative feedback

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