Stability Analysis in a Transmission Line With Nonlinear Elements Using Lyapunov’s Method

Abstract

This paper shows a basic methodology for an equilibrium points based analysis of a nonlinear electrical systems. The purpose is formulate alternative sufficient and necessary conditions to guarantee local asymptotic stability. Equilibrium points take an important role in the modeling and stability analysis of dynamical systems. As a matter of fact, they are the base for developing lot of conceptual tools, like phase portraits, limit cycles, periodic orbits and bifurcation analysis. The modeling and simulation of the effect of a nonlinear oscillator attached to the end of a lumped transmission line parameters is described. The nonlinear oscillator is obtained by a shunt connection between a tunnel diode and a capacitor. The tunnel diode was chosen because is a semiconductor with a negative resistance region, having nonlinear characteristics with multiple equilibrium points. This points of the system were determined through direct application of the Lyapunov’s stability theorems.