A formulation of nonlinear dynamic networks

Some properties on the structure of dynamic equations and a method of systematic formulations of a fairly general class of nonlinear RLC networks and lumped parameter active networks are presented. It is shown that by a differential and integral transformation such that each range of network variables becomes a standard function space, the equation and solution are described by synthetic operators of a certain standard type. The solution is then, definitely computable. Conditions for the unique solvability, which are given by global invertibility of the synthetic operator describing the equation, are derived from the contraction mapping theorem in a Banach space. These conditions are finally expressed in terms of differential coefficients of branch characteristics.