---
tag: 01REYCJ371
kind: concept
name: Lyapunov function
msc: [34D20]
sources:
  - url: https://en.wikipedia.org/wiki/Lyapunov_function
    locator: lead section
same_as:
  wikidata: Q2337858
  wikipedia: Lyapunov function
---

## Summary

A Lyapunov function for an equilibrium of a differential equation is a scalar function with three properties. It is zero at the equilibrium, positive away from it, and non-increasing along solutions.
Its existence proves stability without solving the equation. It is named after Aleksandr Lyapunov. See the [[definition|04P7B5XC22]].