A qualitative investigation of time‐invariant nonlinear networks. Global state equation existence criteria

Abstract

AbstractThis paper defines that globally there exists a state equation when a dynamical system of time‐invariant nonlinear network can be described only by capacitor voltages and inductor currents. A sufficient condition is presented for the state equation to exist globally. A sufficient condition is also shown for the state equation to exist globally, if the capacitor voltage and the inductor currents are replaced by capacitor currents and inductor voltages. Then the effect of the parasitic resistance or parasitic reactance on the existence of the state equation is discussed. When only parasitic resistances are added, the existence of the global state equation is preserved. However, the existence of the global state equation based on the capacitor currents and the inductor voltages is related to the eventual passivity of the original network. The latter half of this paper discusses the effect of perturbation of the branch characteristics constituting the network on the existence of the global state equation. Especially, it is shown that when the element is strictly locally passive, both the existence of the global state equation and the strictly local passivity are not affected by the perturbation.