Practical Stability in terms of Two Measures for Impulsive Differential Equations with "Supremum"
Practical Stability in terms of Two Measures for Impulsive Differential Equations with "Supremum"
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DOI：
10.1155/2011/703189
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发表时间：
2011-01-01
影响因子：
1.6
通讯作者：
Georgieva, A.
中科院分区：
文献类型：
--
作者：
Hristova, S. G.;Georgieva, A.
研究的对象是一个具有“上极值”的脉冲微分方程组。这些方程尚未得到广泛的研究，同时它们是许多现实世界过程的适当数学模型，其中当前状态在很大程度上取决于其在过去时间间隔上的最大值。定义并研究了一类具有“上极值”的非线性脉冲微分方程系统的实际稳定性。将Razumikhin方法应用于分段连续标量Lyapunov函数，并对标量脉冲微分方程进行了比较。为了统一各种稳定性概念，并为稳定性理论的研究提供一个总体框架，本文将双测度稳定性的概念应用于给定系统和比较标量方程。一个例子说明了所得到的充分条件的实用性。
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.