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Article: Polynomial relaxation-based conditions for global asymptotic stability of equilibrium points of genetic regulatory networks

TitlePolynomial relaxation-based conditions for global asymptotic stability of equilibrium points of genetic regulatory networks
Authors
KeywordsBiology
GRN
LMI
PROD form
Stability
SUM form
Issue Date2010
PublisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207721.asp
Citation
International Journal Of Systems Science, 2010, v. 41 n. 1, p. 65-72 How to Cite?
AbstractAn important problem in systems biology consists of establishing whether an equilibrium point of a genetic regulatory network (GRN) is stable or not. This article investigates this problem for GRNs with SUM or PROD regulatory functions. It is shown that sufficient conditions for global asymptotical stability of an equilibrium point of these networks can be derived in terms of convex optimisations with linear matrix inequality constraints. These conditions are obtained by looking for a Lyapunov function through the use of suitable polynomial relaxations, and do not introduce approximations of the nonlinearities present in the GRNs. The benefit of these conditions is that their conservatism can be decreased by increasing the degree of the introduced polynomial relaxations. Numerical examples illustrate the usefulness of the proposed conditions.
Persistent Identifierhttp://hdl.handle.net/10722/129197
ISSN
2015 Impact Factor: 1.947
2015 SCImago Journal Rankings: 1.083
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_HK
dc.date.accessioned2010-12-23T08:33:31Z-
dc.date.available2010-12-23T08:33:31Z-
dc.date.issued2010en_HK
dc.identifier.citationInternational Journal Of Systems Science, 2010, v. 41 n. 1, p. 65-72en_HK
dc.identifier.issn0020-7721en_HK
dc.identifier.urihttp://hdl.handle.net/10722/129197-
dc.description.abstractAn important problem in systems biology consists of establishing whether an equilibrium point of a genetic regulatory network (GRN) is stable or not. This article investigates this problem for GRNs with SUM or PROD regulatory functions. It is shown that sufficient conditions for global asymptotical stability of an equilibrium point of these networks can be derived in terms of convex optimisations with linear matrix inequality constraints. These conditions are obtained by looking for a Lyapunov function through the use of suitable polynomial relaxations, and do not introduce approximations of the nonlinearities present in the GRNs. The benefit of these conditions is that their conservatism can be decreased by increasing the degree of the introduced polynomial relaxations. Numerical examples illustrate the usefulness of the proposed conditions.en_HK
dc.languageengen_US
dc.publisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207721.aspen_HK
dc.relation.ispartofInternational Journal of Systems Scienceen_HK
dc.rightsThis is an electronic version of an article published in International Journal of Systems Science, 2010, v. 41 n. 1, p. 65-72. International Journal of Systems Science is available online at: http://www.informaworld.com/smpp/-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBiologyen_HK
dc.subjectGRNen_HK
dc.subjectLMIen_HK
dc.subjectPROD formen_HK
dc.subjectStabilityen_HK
dc.subjectSUM formen_HK
dc.titlePolynomial relaxation-based conditions for global asymptotic stability of equilibrium points of genetic regulatory networksen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0020-7721&volume=41&issue=1&spage=65&epage=72&date=2010&atitle=Polynomial+relaxation-based+conditions+for+global+asymptotic+stability+of+equilibrium+points+of+genetic+regulatory+networks-
dc.identifier.emailChesi, G:chesi@eee.hku.hken_HK
dc.identifier.authorityChesi, G=rp00100en_HK
dc.description.naturepostprint-
dc.identifier.doi10.1080/00207720903078867en_HK
dc.identifier.scopuseid_2-s2.0-77649256414en_HK
dc.identifier.hkuros176739en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77649256414&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume41en_HK
dc.identifier.issue1en_HK
dc.identifier.spage65en_HK
dc.identifier.epage72en_HK
dc.identifier.isiWOS:000273489600006-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridChesi, G=7006328614en_HK
dc.identifier.citeulike6549508-

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