Constructive Proof of Global Lyapunov Function as Potential Function

Understand

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.