Let me first introduce a positive definite function. Function V : U ⊆ R2 −→ R is said to be positive definite in U if (i) V (0) = 0 and (ii) V (x) > 0 for ...

17 окт. 2007 г. · Let V : Rn → R be a locally positive definite function such that on the compact set Ωr = {x ∈ Rn : V (x) ≤ r} we have˙V (x) ≤ 0. Define.

Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Definition · Basic Lyapunov theorems for... · Example

In the literature on system theory positive definite functions, when used to establish stability, are called Lyapunov functions. Intuitively, their physical ...

Furthermore, if is stable, then a Lyapunov function can always be found by finding the positive-definite solution to the matrix Lyapunov equation (1) P A + A T ...

24 мар. 2017 г. · On everywhere except the origin, V is positive. It is also radially unbounded and vanishes at the origin, which implies V is a Lyapunov function. Condition on output of Lyapunov equation being positive definite How to use Lyapunov Stability theorum if the condition is "for ... Другие результаты с сайта math.stackexchange.com

• positive definite functions. • global Lyapunov stability theorems ... if such a function V exists we call it a Lyapunov function (that proves the.

Example: Positive Definite Function. Positive definite function of two variables. Page 64. 64. Positive Semi-Definite Function---. General Definition. The ...

A continuous function V : Rn × R+ → R is a positive definite function if it satisfies the conditions of Definition 4.4 and, additionally, α(p) → ∞ as p → ∞. To ...

This fictious energy function is known as Lyapunov function and the Lyapunov function should be positive definite function. Lyapunov's stability theorem ...