Piecewise-linear Lyapunov functions for structural stability of biochemical networks
(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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- author
- Blanchini, Franco and Giordano, Giulia LU
- organization
- publishing date
- 2014-10-01
- 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 Press Ltd.
- 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
- 2022-05-02 04:21:04
@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}},
keywords = {{Biochemical networks; Biochemical systems; Global stability; Graph; Piecewise-linear Lyapunov functions; Structural stability}},
language = {{eng}},
month = {{10}},
number = {{10}},
pages = {{2482--2493}},
publisher = {{Pergamon Press Ltd.}},
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}},
doi = {{10.1016/j.automatica.2014.08.012}},
volume = {{50}},
year = {{2014}},
}