Normal Form and Stability of a Class of Coupled Nonlinear Networks

This paper is concerned with the qualitative properties of a subclass of the class of nonlinear R, L, C networks for which there may be mutual coupling among elements of like type. Sufficient conditions are given which guarantee that such a network may be characterized by a set of nonlinear equations in normal form, which indicates a unique response for any excitation. Finally, a study of the stability of networks of this class indicates that for passive networks their asymptotic stability is in one-to-one correspondence with their "weak observability" at the resistor terminals.