Small-signal Stability Criterion for Electrical Networks Containing Lossless Transmission Lines

A stability criterion is derived for networks containing lossless transmission lines as well as the usual lumped electrical elements. The criterion is stated in terms of the transmission line parameters and scattering matrix measurements made at the terminals of the lumped part of the network. The mathematical proof of the stability theorem involves some new results concerning a special system of difference-differential equations. Another stability criterion is derived in terms of more general input-output measurements.