Liapunov's direct method for Birkhoffian systems: Applications to electrical networks

TL;DR

This paper extends Liapunov's direct method to Birkhoffian systems on manifolds, applying it to analyze the stability of linear and nonlinear electrical networks like LC and RLC circuits.

Contribution

It introduces Liapunov's stability analysis within the Birkhoffian framework and constructs specific Liapunov functions for electrical networks.

Findings

Liapunov functions successfully prove stability of electrical networks.

Stability conditions are established for linear and nonlinear circuits.

The method broadens the application of Liapunov's approach to complex dynamical systems.

Abstract

In this paper, the concepts and the direct theorems of stability in the sense of Liapunov, within the framework of Birkhoffian dynamical systems on manifolds, are considered. The Liapunov-type functions are constructed for linear and nonlinear LC and RLC electrical networks, to prove stability under certain conditions.