Practical Stability in terms of Two Measures for Impulsive Differential Equations with "Supremum"

被引：13

作者：

Hristova, S. G. ^{[1
]}

Georgieva, A. ^{[1
]}

机构：

[1] Plovdiv Univ Paisii Hiledarski, Plovdiv 4000, Bulgaria

来源：

INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 2011卷

关键词：

D O I：

10.1155/2011/703189

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The object of investigations is a system of impulsive differential equations with "supremum." These equations are not widely studied yet, and at the same time they are adequate mathematical model of many real world processes in which the present state depends significantly on its maximal value on a past time interval. Practical stability for a nonlinear system of impulsive differential equations with "supremum" is defined and studied. It is applied Razumikhin method with piecewise continuous scalar Lyapunov functions and comparison results for scalar impulsive differential equations. To unify a variety of stability concepts and to offer a general framework for the investigation of the stability theory, the notion of stability in terms of two measures has been applied to both the given system and the comparison scalar equation. An example illustrates the usefulness of the obtained sufficient conditions.

引用

页数：13

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