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Article: On the robust stability of time-varying uncertain genetic regulatory networks

TitleOn the robust stability of time-varying uncertain genetic regulatory networks
Authors
KeywordsGenetic Network
Robustness
Sum Regulatory Function
Time-Varying Uncertainty
Issue Date2011
PublisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/5510
Citation
International Journal Of Robust And Nonlinear Control, 2011, v. 21 n. 15, p. 1778-1790 How to Cite?
AbstractThis paper investigates robust stability of time-varying uncertain genetic regulatory networks (GRNs). In particular, the considered model includes, as special cases, SUM and PROD regulatory functions typically considered in the literature. It is supposed that the coefficients of the GRN are affine linear functions of an uncertain vector constrained in a polytope, and that the activation functions are uncertain into sector-type regions. As the first problem, we consider to establish whether the GRN is robustly globally stable for all admissible uncertainties. It is shown that this problem can be addressed by solving a linear matrix inequality (LMI) feasibility test built by exploiting homogeneous polynomial Lyapunov functions. As the second problem, we consider to determine the slowest speed with which the concentrations of mRNAs and proteins reach their equilibrium values. It is shown that a guaranteed underestimate of such a speed can be provided by solving a generalized eigenvalue problem built from the proposed stability condition. Some numerical examples illustrate the proposed approaches. It is worth remarking that this paper proposes for the first time in the literature the use of nonquadratic Lyapunov functions for studying robust stability of uncertain GRNs, whereas existing works have addressed the problem only via quadratic Lyapunov functions (either common or parameter-dependent), which are known to be conservative for time-varying uncertainty. Copyright © 2011 John Wiley & Sons, Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/155663
ISSN
2015 Impact Factor: 2.527
2015 SCImago Journal Rankings: 2.134
ISI Accession Number ID
Funding AgencyGrant Number
Japan Society for the Promotion of Science (JSPS)
Funding Information:

The authors would like to thank the Associate Editor and the Reviewers for their useful comments that have greatly improved this paper. This research is partially supported by the Japan Society for the Promotion of Science (JSPS) through its "Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)".

References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.contributor.authorChen, Len_US
dc.contributor.authorAihara, Ken_US
dc.date.accessioned2012-08-08T08:34:43Z-
dc.date.available2012-08-08T08:34:43Z-
dc.date.issued2011en_US
dc.identifier.citationInternational Journal Of Robust And Nonlinear Control, 2011, v. 21 n. 15, p. 1778-1790en_US
dc.identifier.issn1049-8923en_US
dc.identifier.urihttp://hdl.handle.net/10722/155663-
dc.description.abstractThis paper investigates robust stability of time-varying uncertain genetic regulatory networks (GRNs). In particular, the considered model includes, as special cases, SUM and PROD regulatory functions typically considered in the literature. It is supposed that the coefficients of the GRN are affine linear functions of an uncertain vector constrained in a polytope, and that the activation functions are uncertain into sector-type regions. As the first problem, we consider to establish whether the GRN is robustly globally stable for all admissible uncertainties. It is shown that this problem can be addressed by solving a linear matrix inequality (LMI) feasibility test built by exploiting homogeneous polynomial Lyapunov functions. As the second problem, we consider to determine the slowest speed with which the concentrations of mRNAs and proteins reach their equilibrium values. It is shown that a guaranteed underestimate of such a speed can be provided by solving a generalized eigenvalue problem built from the proposed stability condition. Some numerical examples illustrate the proposed approaches. It is worth remarking that this paper proposes for the first time in the literature the use of nonquadratic Lyapunov functions for studying robust stability of uncertain GRNs, whereas existing works have addressed the problem only via quadratic Lyapunov functions (either common or parameter-dependent), which are known to be conservative for time-varying uncertainty. Copyright © 2011 John Wiley & Sons, Ltd.en_US
dc.languageengen_US
dc.publisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/5510en_US
dc.relation.ispartofInternational Journal of Robust and Nonlinear Controlen_US
dc.subjectGenetic Networken_US
dc.subjectRobustnessen_US
dc.subjectSum Regulatory Functionen_US
dc.subjectTime-Varying Uncertaintyen_US
dc.titleOn the robust stability of time-varying uncertain genetic regulatory networksen_US
dc.typeArticleen_US
dc.identifier.emailChesi, G:chesi@eee.hku.hken_US
dc.identifier.authorityChesi, G=rp00100en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1002/rnc.1775en_US
dc.identifier.scopuseid_2-s2.0-80053191564en_US
dc.identifier.hkuros201424-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-80053191564&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume21en_US
dc.identifier.issue15en_US
dc.identifier.spage1778en_US
dc.identifier.epage1790en_US
dc.identifier.isiWOS:000295374100005-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridChesi, G=7006328614en_US
dc.identifier.scopusauthoridChen, L=35338963500en_US
dc.identifier.scopusauthoridAihara, K=7103203284en_US

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