Compartmental system analysis: Realization of a class of linear systems with physical constraints

This paper considers the compartmental system analysis from the system theoretic point of view. The specific problem treated here is that of realization of rational transfer function in the form
\dot{x} (t) = Ax(t)+
bu(t), y(t)= c' x(t)
. This problem, however, differs from the usual one in that physical consideration of the compartmental system naturally leads to a set of constraints on the realization. Specifically the matrix
A
is required to satisfy a preassigned sign pattern as well as a diagonal-dominant condition. Realizability conditions and the characterization of minimal realization are discussed in detail. Counter examples are constructed to show that the minimal dimension does not coincide with the McMillan degree of the transfer function. Necessary and sufficient conditions for realizability are obtained when i) the degree of the transfer function is equal to or less than three or ii) the graphical structure of the compartment system is of noncyclic tree type.