A sufficient condition to test identifiability of a nonlinear delayed-differential model with constant delays and multi-inputs

TL;DR

This paper presents a new sufficient condition for testing the identifiability of nonlinear delayed-differential models with constant delays and multiple inputs, extending previous results and combining classical and recent identifiability theories.

Contribution

It introduces a generalized criterion for identifiability of nonlinear delayed-differential models with multiple inputs, based on linearized system analysis and prior theoretical results.

Findings

Provides a sufficient condition for model identifiability.

Extends previous results to models with multiple inputs and delays.

Offers a practical criterion for testing identifiability in complex systems.

Abstract

In this paper, an original result in terms of a sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system and a criterion for linear systems with constant delays is provided, from which the identifiability of the original nonlinear system can be proved. This result is obtained by combining a classical identifiability result for nonlinear ordinary differential systems due to M.S. Grewal and K. Glover (1976) with the identifiability of linear delayed-differential models developed by Y. Orlov et al. (2002). This paper is a generalization of the results provided by L. Denis-Vidal, C. Jauberthie, G. Joly-Blanchard (2006), which deal with the specific case of nonlinear delayed-differential models with two delays and a single input.