##  [Lyapunov Function](/lyapunov-function) 

  ##  [Lyapunov Function](https://natural.quantumdictionary.io/lyapunov-function-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A scalar-valued function V(x) defined on a neighbourhood of an equilibrium of a dynamical system that is positive-definite and whose derivative along system trajectories has a definite sign (typically nonincreasing), used as a certificate of stability without solving trajectories.