On the Stability of Interconnected Systems*

Theorems are presented concerning conditions for the input-output stability of interconnected dynamical systems. Results in the area of input-output stability are often partitioned into two categories: small-gain type-results and passivity-type results. The main theorem given here does not fall into either of these categories, but is most closely related to the passivity-type results. The theorem involves a new class of interconnection operators that is a substantial generalization of the familiar set of nonnegative operators defined on a space of vector-valued functions.