On the construction of a matrix-valued Lyapunov function for a linear periodic system on a time scale

被引：1

作者：

Martynyuk, A. A. ^{[1
]}

Slyn'ko, V. I. ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Timoshenko Inst Mech, UA-03057 Kiev, Ukraine

来源：

DOKLADY MATHEMATICS | 2007年 / 76卷 / 03期

关键词：

Asymptotic Stability; Operator Equation; DOKLADY Mathematic; Fredholm Integral Equation; Jump Operator;

D O I：

10.1134/S1064562407060038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A method for constructing a matrix-valued function for a linear large-scale system on a time scale has been described. The approach allows to solve the stability problem for linear periodic systems on the basis of the generalized Lyapunov direct method. A generalized integral equation for the elements of the matrix-valued Lyapunov function is achieved by changing the order of integration. The construction of the elements of the matrix valued Lyapunov function has also been reduced to solve the generalized Fredholm integral equation.

引用

页码：812 / 816

页数：5

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