Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system

Handle URI:
http://hdl.handle.net/10754/594256
Title:
Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system
Authors:
N’Doye, Ibrahima; Voos, Holger; Darouach, Mohamed; Schneider, Jochen G.
Abstract:
This paper presents the ℋ∞ static output feedback control of nonlinear fractional-order systems. Based on the extended bounded real lemma, the ℋ∞ control is formulated and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order α belongs to 0 < α < 1. The control approach is finally applied to the regulation of the glucose level in diabetes type 1 treatment. Therefore, it is attempted to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of the system in the presence of meal disturbance. Numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart in the presence of exogenous glucose infusion or meal disturbance. © 2015 Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
N’Doye I, Voos H, Darouach M, Schneider JG (2015) Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system. Int J Control Autom Syst 13: 798–807. Available: http://dx.doi.org/10.1007/s12555-013-9192-y.
Publisher:
Springer Science + Business Media
Journal:
International Journal of Control, Automation and Systems
Issue Date:
23-May-2015
DOI:
10.1007/s12555-013-9192-y
Type:
Article
ISSN:
1598-6446; 2005-4092
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorN’Doye, Ibrahimaen
dc.contributor.authorVoos, Holgeren
dc.contributor.authorDarouach, Mohameden
dc.contributor.authorSchneider, Jochen G.en
dc.date.accessioned2016-01-19T14:44:30Zen
dc.date.available2016-01-19T14:44:30Zen
dc.date.issued2015-05-23en
dc.identifier.citationN’Doye I, Voos H, Darouach M, Schneider JG (2015) Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system. Int J Control Autom Syst 13: 798–807. Available: http://dx.doi.org/10.1007/s12555-013-9192-y.en
dc.identifier.issn1598-6446en
dc.identifier.issn2005-4092en
dc.identifier.doi10.1007/s12555-013-9192-yen
dc.identifier.urihttp://hdl.handle.net/10754/594256en
dc.description.abstractThis paper presents the ℋ∞ static output feedback control of nonlinear fractional-order systems. Based on the extended bounded real lemma, the ℋ∞ control is formulated and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order α belongs to 0 < α < 1. The control approach is finally applied to the regulation of the glucose level in diabetes type 1 treatment. Therefore, it is attempted to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of the system in the presence of meal disturbance. Numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart in the presence of exogenous glucose infusion or meal disturbance. © 2015 Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelbergen
dc.publisherSpringer Science + Business Mediaen
dc.subjectDiabetes controlen
dc.subjectfractional calculusen
dc.subjectfractional-order modelen
dc.subjectlinear matrix inequality (LMI)en
dc.subjectLyapunov fractionalen
dc.subjectminimal model of glucose-insulinen
dc.subjectstatic output feedbacken
dc.subjectℋ<inf>∞</inf> controlen
dc.titleStatic output feedback ℋ ∞ control for a fractional-order glucose-insulin systemen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalInternational Journal of Control, Automation and Systemsen
dc.contributor.institutionFaculty of Science, Technology and Communication (FSTC), University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, Luxembourg, Luxembourgen
dc.contributor.institutionResearch Center for Automatic Control of Nancy (CRAN UMR, 7039, CNRS), IUT de Longwy, University of Lorraine, 186 rue de Lorraine, Cosnes et Romain, Franceen
dc.contributor.institutionLuxembourg Centre for Systems Biomedicine, University of Luxembourg, 7, Avenue des hauts Fournaux, Belval, Luxembourgen
kaust.authorNdoye, Ibrahimaen
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