Abstract
This work presents existence and uniqueness theorems for the currents and voltages in a countably infinite RLC electrical network for which the total power dissipated in all the resistors or stored in all the capacitors and inductors is allowed to be infinite. This relaxation of the finite-power condition prevents the use of a number of Hilbert-space techniques and requires instead a more graph-theoretical approach. The latter has previously been used to analyze linear time-invariant networks. The main contribution of the present work is that it encompasses, under certain conditions, time-varying active networks with nonlinear resistors, inductors, and capacitors.
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