Stability of the linearization method in compartmental analysis

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

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.

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.

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.