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Structural stability of biochemical networks : Quadratic vs. polyhedral Lyapunov functions

Blanchini, Franco and Giordano, Giulia LU (2015) 8th IFAC Symposium on Robust Control Design, ROCOND 2015 In IFAC Proceedings Volumes (IFAC-PapersOnline) 48. p.278-283
Abstract

Due to the intrinsic uncertainty and variability affecting biochemical reaction networks, it is fundamental to assess their structural stability, i.e., to establish if all the networks having a given structure are stable independent of specific parameter values. For basic motifs in biochemical networks, we show that stability cannot be structurally proved by quadratic Lyapunov functions. However, structural stability of these motifs can be shown resorting to piecewise-linear Lyapunov functions, based on the results by Blanchini and Giordano (2014), who provide a theoretical framework and efficient numerical methods to evaluate structural stability of biochemical reaction networks with monotone reaction rates.

Please use this url to cite or link to this publication:
author
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Biochemical networks, Biochemical systems, Graph, Piecewise-linear Lyapunov functions, Quadratic Lyapunov functions, Structural stability
in
IFAC Proceedings Volumes (IFAC-PapersOnline)
volume
48
pages
6 pages
publisher
IFAC Secretariat
conference name
8th IFAC Symposium on Robust Control Design, ROCOND 2015
external identifiers
  • Scopus:84954146969
DOI
10.1016/j.ifacol.2015.09.470
language
English
LU publication?
no
id
8aa2513d-d80b-441a-9dc5-7fd3c0f2ab58
date added to LUP
2016-07-06 15:21:05
date last changed
2016-07-11 10:02:38
@inproceedings{8aa2513d-d80b-441a-9dc5-7fd3c0f2ab58,
  abstract     = {<p>Due to the intrinsic uncertainty and variability affecting biochemical reaction networks, it is fundamental to assess their structural stability, i.e., to establish if all the networks having a given structure are stable independent of specific parameter values. For basic motifs in biochemical networks, we show that stability cannot be structurally proved by quadratic Lyapunov functions. However, structural stability of these motifs can be shown resorting to piecewise-linear Lyapunov functions, based on the results by Blanchini and Giordano (2014), who provide a theoretical framework and efficient numerical methods to evaluate structural stability of biochemical reaction networks with monotone reaction rates.</p>},
  author       = {Blanchini, Franco and Giordano, Giulia},
  booktitle    = {IFAC Proceedings Volumes (IFAC-PapersOnline)},
  keyword      = {Biochemical networks,Biochemical systems,Graph,Piecewise-linear Lyapunov functions,Quadratic Lyapunov functions,Structural stability},
  language     = {eng},
  month        = {07},
  pages        = {278--283},
  publisher    = {IFAC Secretariat},
  title        = {Structural stability of biochemical networks : Quadratic vs. polyhedral Lyapunov functions},
  url          = {http://dx.doi.org/10.1016/j.ifacol.2015.09.470},
  volume       = {48},
  year         = {2015},
}