Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates

Franco Blanchini; Giulia Giordano

doi:10.1109/CDC.2015.7402687

Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates

Franco Blanchini, Giulia Giordano

ELLIIT: the Linköping-Lund initiative on IT and mobile communication

University of Udine

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

Abstract

Structural properties, independent of specific parameter values, can explain the robustness of biochemical systems. In this paper we consider the framework previously proposed by the authors to assess structural stability of biochemical reaction networks with monotone reaction rates, which considers systems in concentration coordinates, and we show that the results can be applied to systems in reaction coordinates (whose stability was first investigated by Al-Radhawi and Angeli): the same numerical test can be employed to find a polyhedral Lyapunov function and thus certify stability. Under suitable assumptions on the rank of structural matrices, we prove the equivalence between the test performed for the system in concentration coordinates and in reaction coordinates. We finally illustrate the approach by examples.

Original language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Publisher	IEEE - Institute of Electrical and Electronics Engineers Inc.
Pages	3110-3115
Number of pages	6
ISBN (Print)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7402687
Publication status	Published - 2015 Dec
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: 2015 Dec 15 → 2015 Dec 18 Conference number: 54

Conference

Conference	54th IEEE Conference on Decision and Control, CDC 2015
Abbreviated title	CDC 2015
Country/Territory	Japan
City	Osaka
Period	2015/12/15 → 2015/12/18

Subject classification (UKÄ)

Control Engineering

Access to Document

10.1109/CDC.2015.7402687

Cite this

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title = "Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates",

abstract = "Structural properties, independent of specific parameter values, can explain the robustness of biochemical systems. In this paper we consider the framework previously proposed by the authors to assess structural stability of biochemical reaction networks with monotone reaction rates, which considers systems in concentration coordinates, and we show that the results can be applied to systems in reaction coordinates (whose stability was first investigated by Al-Radhawi and Angeli): the same numerical test can be employed to find a polyhedral Lyapunov function and thus certify stability. Under suitable assumptions on the rank of structural matrices, we prove the equivalence between the test performed for the system in concentration coordinates and in reaction coordinates. We finally illustrate the approach by examples.",

author = "Franco Blanchini and Giulia Giordano",

year = "2015",

month = dec,

doi = "10.1109/CDC.2015.7402687",

language = "English",

isbn = "9781479978861",

pages = "3110--3115",

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

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

address = "United States",

note = "54th IEEE Conference on Decision and Control, CDC 2015, CDC 2015 ; Conference date: 15-12-2015 Through 18-12-2015",

}

Blanchini, F & Giordano, G 2015, Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates. in Proceedings of the IEEE Conference on Decision and Control., 7402687, IEEE - Institute of Electrical and Electronics Engineers Inc., pp. 3110-3115, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 2015/12/15. https://doi.org/10.1109/CDC.2015.7402687

Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates. / Blanchini, Franco; Giordano, Giulia.
Proceedings of the IEEE Conference on Decision and Control. IEEE - Institute of Electrical and Electronics Engineers Inc., 2015. p. 3110-3115 7402687.

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

TY - GEN

T1 - Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates

AU - Blanchini, Franco

AU - Giordano, Giulia

N1 - Conference code: 54

PY - 2015/12

Y1 - 2015/12

N2 - Structural properties, independent of specific parameter values, can explain the robustness of biochemical systems. In this paper we consider the framework previously proposed by the authors to assess structural stability of biochemical reaction networks with monotone reaction rates, which considers systems in concentration coordinates, and we show that the results can be applied to systems in reaction coordinates (whose stability was first investigated by Al-Radhawi and Angeli): the same numerical test can be employed to find a polyhedral Lyapunov function and thus certify stability. Under suitable assumptions on the rank of structural matrices, we prove the equivalence between the test performed for the system in concentration coordinates and in reaction coordinates. We finally illustrate the approach by examples.

AB - Structural properties, independent of specific parameter values, can explain the robustness of biochemical systems. In this paper we consider the framework previously proposed by the authors to assess structural stability of biochemical reaction networks with monotone reaction rates, which considers systems in concentration coordinates, and we show that the results can be applied to systems in reaction coordinates (whose stability was first investigated by Al-Radhawi and Angeli): the same numerical test can be employed to find a polyhedral Lyapunov function and thus certify stability. Under suitable assumptions on the rank of structural matrices, we prove the equivalence between the test performed for the system in concentration coordinates and in reaction coordinates. We finally illustrate the approach by examples.

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U2 - 10.1109/CDC.2015.7402687

DO - 10.1109/CDC.2015.7402687

M3 - Paper in conference proceeding

AN - SCOPUS:84962019278

SN - 9781479978861

SP - 3110

EP - 3115

BT - Proceedings of the IEEE Conference on Decision and Control

PB - IEEE - Institute of Electrical and Electronics Engineers Inc.

T2 - 54th IEEE Conference on Decision and Control, CDC 2015

Y2 - 15 December 2015 through 18 December 2015

ER -

Polyhedral Lyapunov functions for structural stability of biochemical systems in concentration and reaction coordinates

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