On the uniqueness of the steady state for nonlinear circuits with time-dependent sources

Circuits composed of a strongly locally passive resistive - port that is terminated with strongly locally passive two- or multiterminal capacitors and inductors and bounded voltage and current sources are considered. They are shown to have a unique steady state if a certain, explicitly given inequality is satisfied. Under the same condition, the exponential decay of the transients is shown, and an explicit lower bound for its rate is given. The analysis shows that the more the resistive -port is locally passive, the more the reactive elements can become nonlinear while the steady state remains unique. For the special case of a linear reciprocal resistive -port, a less restrictive inequality is derived.