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Abstract:

Purpose – The purpose of this paper is to prove that under sufficient conditions the linearization method used for identifying a nonlinear bicompartmental system is stable.

Design/methodology/approach – The problem of identifying a nonlinear compartmental system appears as badly stated a priori. In fact the problem is not to identify the general behavior law of exchange between compartments, but to assume these laws known such as in Michaelis-Menten systems or in polynomial compartmental systems with coefficients that need to be identified. It has been proved previously that with a linearization method an approximation can be obtained to the identification of these nonlinear systems. To validate this method, a stability study is necessary.

Findings – Sufficient conditions are established for the evolution law of a nonlinear bicompartmental system under which the linearization method is stable, and an upper bound is given on the approximation error – with an application, in the last section to the case of an open Michaelis-Menten system.

Originality/value – The paper is of value in establishing sufficient conditions about the evolution law of a nonlinear system in order to show that this method is stable and to give an upper bound on the approximation error.

Keywords:

Cybernetics, Linear structure equation modelling, Modelling, Numerical analysis

Article Type:

Research paper

Article URL:

http://www.emeraldinsight.com/10.1108/03684920910962641

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