A General Theorem for the Existence and Solution of State Models for Linear, Stationary Systems of Multi-Terminal Components

Abstract

Two alternate statements of a fundamental theorem on existence of state models and their solutions for systems of multi-terminal, linear, stationary components are presented in terms of the system structure, i.e., the component characteristics and their topology. The theorems, along with their proof, establish an explicit procedure for 1) identifying an upper bound on the order of the system state vector, 2) identifying the components in the state vector, 3) generating the system state model, and 4) developing state models of hierarchies of system components, i.e., the solution of large-scale systems by "tearing and reconstruction." Six corollaries to the main theorem simplify its application for many of the systems encountered in practice.