Compartmental modeling and power flow analysis for state space systems

A connection between arbitrary (not necessarily nonnegative) state space systems and compartmental models is discussed. 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 is used to derive the dynamics of the diagonal elements of the second-moment matrix which satisfies a Lyapunov differential equation. Conditions under which the steady-state values of the diagonal elements satisfy a steady-state compartmental model are given