Convergence properties of nonlinear RLC electrical networks

Abstract

Convergence properties of general electrical networks with grounded nonlinear capacitors at the nodes and nonlinear inductors and resistors at the edges are studied. It is shown how, under appropriate conditions, for every initial condition there exists a unique equilibrium to which the system converges asymptotically. Partial extensions to networks with terminals or current sources are also provided. For RC networks this is compared with the use of an alternative storage function based on the co-content functions of the resistors.