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

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

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A stability-analysis method that constructs scalar Lyapunov functions—real-valued functions on the state space—whose sign and time derivative along system trajectories provide certificates of stability, asymptotic behavior, or instability for deterministic dynamical systems.