Constructive Proof of Global Lyapunov Function as Potential Function
Chaotic Dynamics
2014-03-26 v1 Mathematical Physics
math.MP
Abstract
We provide a constructive proof on the equivalence of two fundamental concepts: the global Lyapunov function in engineering and the potential function in physics, establishing a bridge between these distinct fields. This result suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems through the analogy with existing methods on potential functions. In addition, we show another connection that the Lyapunov equation is a reduced form of the generalized Einstein relation for linear systems.
Cite
@article{arxiv.1012.2721,
title = {Constructive Proof of Global Lyapunov Function as Potential Function},
author = {Ruoshi Yuan and Yian Ma and Bo Yuan and Ping Ao},
journal= {arXiv preprint arXiv:1012.2721},
year = {2014}
}
Comments
4 pages