含Causal算子的脉冲微分方程的两度量稳定性

Stability for Impulsive Differential Systems with Causal Operators in Terms of Two Measures

脉冲微分方程理论是微分方程理论的一个重要分支,相对于微分方程理论而言,脉冲微分方程理论有着更为广泛的应用,因此许多研究者对此产生了浓厚的兴趣,其中脉冲微分方程的稳定性是其理论中的重要分支。本文引入函数上拟单调的概念,并建立了新的比较原理,运用这个比较原理和李雅普诺夫函数,从而得到了含有causal算子的脉冲微分系统的两度量稳定性的一些判据,从而丰富了脉冲微分系统的研究结果。

Impulse differential equation theory is an important branch of differential equation theory. Compared with differential equation theory, impulse differential equation theory has a wider range of applications, among which the stability of impulse differential equation is an important branch of its theory, so many researchers have a keen interest in it. In this paper, a new concept of quasi-monotone function is introduced, and a new comparison principle is also established. By using this principle and Lyapunov functions, some criteria about stability for impulsive differential equations with causal operators in terms of two measures are obtained. This enriches the research results of impulsive differential systems.