Authors:
Farida Benmakrouha
1
;
Christiane Hespel
1
;
Mikhail V. Foursov
2
and
Jean-Pierre Hespel
3
Affiliations:
1
IRISA-INSA, France
;
2
IRISA-Universite de Rennes-1, France
;
3
Centre Hospitalier Universitaire de Rennes, France
Keyword(s):
Dynamical system, Bilinear model, Regulation, Stability, Insulin perfusion.
Related
Ontology
Subjects/Areas/Topics:
Biocomputing and Biochips
;
Biomedical Engineering
;
Biomedical Instruments and Devices
;
Devices
;
Health Monitoring Devices
;
Human-Computer Interaction
;
Physiological Computing Systems
Abstract:
We study the Bounded-Input-Bounded-Output (BIBO) stability of the system modeling the behavior “insulin delivery/glycaemia” of the diabetic patient, under continuous insulin infusion, continuous glucose monitoring, in order to point out that the patient is entering in a period of stable/unstable equilibrium.
The model is a bilinear dynamical system predicting for an interval of 15 minutes, with an average error of 15%. In case of stable equilibrium, the prediction will be valid for a longer time interval, when in case of unstable equilibrium, it will leads one to reduce the time intervals.
The BIBO stability is studied by computing the generating series G of the model. This series, generalization of the transfer fuction, is a tool for analyzing the stability of bilinear systems. It is a rational power series in noncommutative variables and by evaluating it, a formal expression of the output in form of iterated integrals is provided. Three cases arise: firstly, the output can be exp
licitly computed; secondly, the output can be bounded/unbounded if the input is bounded; thirdly, no conclusion seems available about the BIBO stability by using G. We propose a stabilizing constant input h by studying the univariate series Gh.
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