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{{short description|Concept in the analysis of dynamical systems}}
In the theory of [[ordinary differential equations]] (ODEs), '''Lyapunov functions''' are scalar functions that may be used to prove the stability of an [[equilibrium point|equilibrium]] of an ODE. Named after the [[Russia]]n [[mathematician]] [[Aleksandr Lyapunov|Aleksandr Mikhailovich Lyapunov]], Lyapunov functions (also called the Lyapunov’s second method for stability) are important to [[stability theory]] of [[dynamical system]]s and [[control theory]]. A similar concept appears in the theory of general state space [[Markov chain]]s, usually under the name Foster–Lyapunov functions.
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