Is a system representable as a compartmental system?

The process of assessing the compartmental nature of a system under analysis involves a number of different professional skills. The first basic question is: given an experiment, i.e. an input-output sequence, and suppose there is no error in the data, is the result compatible with the compartmental assumption? In this paper, a step toward the solution of this fundamental problem is reported by proving necessary and sufficient conditions for a given transfer function to be the one of a finite dimensional deterministic, linear and open compartmental system with constant fractional transfer coefficients.