Stability and instability criteria for nonlinear distributed networks

Electrical networks consisting of lumped linear and memoryless nonlinear elements and an arbitrary number of lossless transmission lines are considered. It is shown that a large class of such networks can be described by a system of functional-differential equations having the form , where the state of the system at time is represented by , a point in the space of bounded continuous functions mapping the interval into , with the compact open topology, and the function mapping into is continuous and Lipschitzian. A Lyapunov functional is presented and used to obtain several theorems concerning the stability and instability of the equilibrium solution of such networks.