This is the author's accepted versionFinal version available from Elsevier via the DOI in this recordWe present two linked theorems on passivity: the passive behavior theorem, parts 1 and 2. Part 1 provides necessary and sufficient conditions for a general linear system, described by a set of high order differential equations, to be passive. Part 2 extends the positive-real lemma to include uncontrollable and unobservable state-space systems.This research was conducted in part during a Fellowship supported by the Cambridge Philosophical Society , http://www.cambridgephilosophicalsociety.org
