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In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions (also called the Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions.

In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions (also called the Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions.

在<font color="#ff8000">常微分方程 ordinary differential equations</font>理论中，<font color="#ff8000">李雅普诺夫函数 Lyapunov functions</font>是可用来证明常微分方程<font color="#ff8000">平衡点 equilibrium point</font>稳定性的标量函数。以俄罗斯数学家亚历山大·李亚普诺夫的名字命名的李雅普诺夫函数(也称为李雅普诺夫稳定性的第二种方法)对于<font color="#ff8000">动态系统 dynamical system</font>的<font color="#ff8000">稳定性理论 stability theory</font>和<font color="#ff8000">控制论 control theory</font>是很重要的。在一般状态空间<font color="#ff8000">马尔可夫链 Markov chains</font>理论中也出现了类似的概念，通常称为 Foster-Lyapunov 函数。

在<font color="#ff8000">常微分方程 ordinary differential equations</font>理论中，<font color="#ff8000">李雅普诺夫函数 Lyapunov functions</font>是可用来证明常微分方程<font color="#ff8000">平衡点 equilibrium point</font>稳定性的标量函数。以俄罗斯数学家亚历山大·李亚普诺夫的名字命名的李雅普诺夫函数(也称为稳定性的李雅普诺夫第二种方法)对于<font color="#ff8000">动态系统 dynamical system</font>的<font color="#ff8000">稳定性理论 stability theory</font>和<font color="#ff8000">控制论 control theory</font>是很重要的。在一般状态空间<font color="#ff8000">马尔可夫链 Markov chains</font>理论中也出现了类似的概念，通常称为 Foster-Lyapunov 函数。