Constructive Proof of Global Lyapunov Function as Potential Function

2010/12/13 by Ruoshi Yuan, Yian Ma, Bo Yuan +1 · 2 citations
Physics and Astronomy · Mathematics · #nlin.CD #math-ph #math.MP

paper · pdf · doi:10.1088/1674-1056/23/1/010505

published as Chin. Phys. B 23 (1), 010505, 2014 · 4 pages

arxiv created 2010/12/13 · arxiv updated 2014/03/26

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.

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