标题：Razumikhin and Krasovskii methods for asymptotic stability of nonlinear delay impulsive systems on time scales
作者：Zhang, Xianfu; Lu, Xiaodong; Liu, Zhi
作者机构：[Zhang, Xianfu; Lu, Xiaodong; Liu, Zhi] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China.
通讯作者：Lu, Xiaodong;Lu, XD
通讯作者地址：[Lu, XD]Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China.
来源：NONLINEAR ANALYSIS-HYBRID SYSTEMS
关键词：Razumikhin and Krasovskii methods; Nonlinear delay impulsive system;; Asymptotic stability; Time scale
摘要：In this paper, asymptotic stability problems of nonlinear delay impulsive systems on time scales are considered based on the Razumikhin and Krasovskii methods. First, a Krasovskii-type theorem is provided for uniform asymptotic stability and uniform exponential stability of delay impulsive systems on time scales. It is shown that this Krasovskii stability criterion does not require the time derivative of the Lyapunov functional to be necessarily nonpositive on each impulsive interval. Second, asymptotic stability problems of delay impulsive systems on time scales is investigated based on the Razumikhin approach. The advantage of this method is that the length of each impulse interval does not depend on the time delay, which results in the fact that the state trajectory may not decrease instantly and sharply at each impulsive point. Moreover, the idea of this paper provides a unified approach to study continuous system and its discrete counterpart simultaneously. An example is given for illustrating the effectiveness of the proposed results. (C) 2018 Elsevier Ltd. All rights reserved.