论文标题
关于通用线性微分方程和应用于冲动系统的应用的稳定性
On stability for generalized linear differential equations and applications to impulsive systems
论文作者
论文摘要
在本文中，我们有兴趣研究广义线性微分方程（GLDES）的稳定性概念。最初，我们提出并重新审视稳定性的几个定义，并根据过渡矩阵的上限和渐近行为提供了它们的完整表征。此外，我们说明了GLDES对线性周期系统和线性冲动微分方程的稳定性结果。最后，我们证明，均匀渐近稳定性和变异渐近稳定性的众所周知的定义等效于本文中引入的全球统一指数稳定性。
In this paper, we are interested in investigating notions of stability for generalized linear differential equations (GLDEs). Initially, we propose and revisit several definitions of stability and provide a complete characterisation of them in terms of upper bounds and asymptotic behaviour of the transition matrix. In addition, we illustrate our stability results for GLDEs to linear periodic systems and linear impulsive differential equations. Finally, we prove that the well known definitions of uniform asymptotic stability and variational asymptotic stability are equivalent to the global uniform exponential stability introduced in this article.
