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Piecewise-linear Lyapunov functions for structural stability of biochemical networks

Blanchini, Franco and Giordano, Giulia LU (2014) In Automatica 50(10). p.2482-2493
Abstract

We consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates, namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values. We investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral Lyapunov function proper to the considered network structure. A numerical recursive procedure is devised to test stability. For a wide class of mono- and bimolecular reaction networks, which we name unitary, the procedure is shown to be very efficient since, due to the particular structure of the problem, it requires iterations in the space of integer-valued matrices. We also... (More)

We consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates, namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values. We investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral Lyapunov function proper to the considered network structure. A numerical recursive procedure is devised to test stability. For a wide class of mono- and bimolecular reaction networks, which we name unitary, the procedure is shown to be very efficient since, due to the particular structure of the problem, it requires iterations in the space of integer-valued matrices. We also consider a similar, less conservative procedure that allows us to test, even when the Lyapunov function cannot be found, whether the system evolution is structurally bounded. In this case, we absorb the equations in a positive linear differential inclusion. To show the effectiveness of the proposed procedure, we report the outcomes of both a stability and a boundedness test, for many non-trivial biochemical reaction networks, and we analyze well established models in the literature.

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Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Biochemical networks, Biochemical systems, Global stability, Graph, Piecewise-linear Lyapunov functions, Structural stability
in
Automatica
volume
50
issue
10
pages
12 pages
publisher
Pergamon
external identifiers
  • scopus:84908136789
ISSN
0005-1098
DOI
10.1016/j.automatica.2014.08.012
language
English
LU publication?
no
id
71f1a7c9-fadf-40e9-8fca-9cfe9a7fed1d
date added to LUP
2016-07-06 15:27:35
date last changed
2017-03-26 04:43:47
@article{71f1a7c9-fadf-40e9-8fca-9cfe9a7fed1d,
  abstract     = {<p>We consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates, namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values. We investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral Lyapunov function proper to the considered network structure. A numerical recursive procedure is devised to test stability. For a wide class of mono- and bimolecular reaction networks, which we name unitary, the procedure is shown to be very efficient since, due to the particular structure of the problem, it requires iterations in the space of integer-valued matrices. We also consider a similar, less conservative procedure that allows us to test, even when the Lyapunov function cannot be found, whether the system evolution is structurally bounded. In this case, we absorb the equations in a positive linear differential inclusion. To show the effectiveness of the proposed procedure, we report the outcomes of both a stability and a boundedness test, for many non-trivial biochemical reaction networks, and we analyze well established models in the literature.</p>},
  author       = {Blanchini, Franco and Giordano, Giulia},
  issn         = {0005-1098},
  keyword      = {Biochemical networks,Biochemical systems,Global stability,Graph,Piecewise-linear Lyapunov functions,Structural stability},
  language     = {eng},
  month        = {10},
  number       = {10},
  pages        = {2482--2493},
  publisher    = {Pergamon},
  series       = {Automatica},
  title        = {Piecewise-linear Lyapunov functions for structural stability of biochemical networks},
  url          = {http://dx.doi.org/10.1016/j.automatica.2014.08.012},
  volume       = {50},
  year         = {2014},
}