ABSTRACT
Compartmental modules involve nonnegative state variables that exchange mass, energy, or other quantities in accordance with conservation laws. Such models are widespread in biology and economics. In this paper a connection is made between arbitrary (not necessarily nonnegative) state space systems and compartmental models. Specifically, a dynamical model is obtained for the nonnegative diagonal elements of the nonnegative-definite second -moment matrix, which arises from an additive white noise model. Kronecker and Hadamard (Schur) matrix algebra are used to derive the dynamics of the diagonal elements of the second-moment matrix which satisfies a Lyapunov differential equation. The paper then provides conditions under which the steady-state values of the diagonal elements satisfy a steady-state compartmental model.
