Compositional properties of passivity

The classical passivity theorem states that the negative feedback interconnection of passive systems is again passive. The converse statement, - passivity of the interconnected system implies passivity of the subsystems -, turns out to be equally valid. This result implies that among all feasible storage functions of a passive interconnected system there is always one that is the sum of storage functions of the subsystems. Sufficient conditions guaranteeing that all storage functions are of this type are derived. Closely related is the question when and how the stability of the closed-loop interconnected system implies passivity of the subsystems. We recall a folklore theorem which was proved for SISO linear systems, and derive some preliminary results towards a more general result, using the theory of simulation relations.