更改

== Definition of a Lyapunov function==

== Definition of a Lyapunov function 李雅普诺夫函数的定义==

A Lyapunov function for an autonomous [[dynamical system]]  

A Lyapunov function for an autonomous [[dynamical system]]  

A Lyapunov function for an autonomous dynamical system  

A Lyapunov function for an autonomous dynamical system  

with an equilibrium point at <math>y=0</math> is a scalar function <math>V:\R^n\to\R</math> that is continuous, has continuous first derivatives, is locally positive-definite, and for which <math>-\nabla{V}\cdot g</math> is also locally positive definite. The condition that <math>-\nabla{V}\cdot g</math> is locally positive definite is sometimes stated as <math>\nabla{V}\cdot g</math> is locally negative definite.  

with an equilibrium point at <math>y=0</math> is a scalar function <math>V:\R^n\to\R</math> that is continuous, has continuous first derivatives, is locally positive-definite, and for which <math>-\nabla{V}\cdot g</math> is also locally positive definite. The condition that <math>-\nabla{V}\cdot g</math> is locally positive definite is sometimes stated as <math>\nabla{V}\cdot g</math> is locally negative definite.  

在 math y 0 / math 上的平衡点是一个标量函数数学 v: r ^ n 到 r / math，它是连续的，有连续的一阶导数，是局部正定的，对于它，math-abla { v } cdot g / math 也是局部正定的。有时把 math-abla { v }-cdot g / math 局部正定的条件表述为 math-abla { v }-cdot g / math 局部负定。

<math>y=0</math> 是它的一个平衡点，其李雅普诺夫函数是一个标量函数：<math>V:\R^n\to\R</math>，它是连续的并且有连续的一阶导数，且是局部正定的，以及<math>-\nabla{V}\cdot g</math>也是局部正定的。有时把 <math>-\nabla{V}\cdot g</math> 局部正定的条件表述为 <math>\nabla{V}\cdot g</math> 是局部负定的。

 

<math>H(x) > 0 \quad \forall x \in \mathcal{B} \setminus\{0\} .</math>

<math>H(x) > 0 \quad \forall x \in \mathcal{B} \setminus\{0\} .</math>

数学 h (x)0对于数学中的所有 x-0. /  

数学 h (x)0对于数学中的所有 x-0. /

 

 

== Basic Lyapunov theorems for autonomous systems==

== Basic Lyapunov theorems for autonomous systems==