Can any reduced order model be obtained via projection?

The paper investigates the properties of general reduced order models obtained by projection of a high order system. It answers questions such as are any two models of different orders related by a projection? Is it possible to obtain the same reduced order model using different projections? How to find, if it exists, a projection that relates the two models? It is shown that answers to those questions can be obtained by investigating the properties of a certain matrix pencil. In case the system is square the problem becomes that of a generalized eigenvalue, and in non-square systems the key tool is the Kronecker Canonical Form.