Stability of passive time-variable circuits

Lyapunov´s second method is used to show that circuits composed of a finite connection of linear, passive, time-variable elements are necessarily stable. Such connections may involve transformers and gyrators as circuit elements, as well as the conventional resistors, inductors and capacitors. An equivalent structure is determined, using only time-variable gyrators to interconnect constant elements consisting of unit capacitors and unit resistors. Using this model, asymptotic stability and uniform asymptotic stability of the original circuit may be investigated. Examples are given to illustrate the methods and concepts.