SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3763-3784, January 2020.
In the paper, we investigate the exponential stability of nonlinear delayed systems with destabilizing and stabilizing delayed impulses, respectively. Specifically, the study can be divided into two cases: (1) stability of delayed systems with destabilizing delayed impulses, where the time delays in impulses can be flexible and even larger than the length of impulsive interval, and (2) stability of delayed systems with stabilizing delayed impulses, where the time delays in impulses are flexible between two consecutive impulsive instants. In order to address the time-delay term in impulses, the concept of average impulsive delay (AID) is proposed. Using the ideas of average impulsive interval and AID, we present some Lyapunov-based exponential stability criteria for delayed systems with average-delay impulses, where the delays in impulses satisfy the proposed AID condition. It is shown that time delay in impulse has double effects, namely, it may destabilize a stable system or stabilize an unstable system. Interestingly, it is also shown that for some stable delayed systems with stabilizing delayed impulses, under certain conditions, the stability can be ensured regardless of the size of delay in continuous dynamics. Further, we apply the theoretical results to the impulsive synchronization control of Chua's circuits with both transmission delay and sampling delay. Finally, some examples are given to illustrate the validity of the derived results.

中文翻译：

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具有平均延迟脉冲的时滞系统的指数稳定性

SIAM控制与优化杂志，第58卷，第6期，第3763-3784页，2020年1月。
在本文中，我们研究了带有时滞和时滞稳定脉冲的非线性时滞系统的指数稳定性。具体来说，该研究可以分为两种情况：（1）具有不稳定的延迟脉冲的延迟系统的稳定性，其中脉冲的时间延迟可以是灵活的，甚至大于脉冲间隔的长度，（2）延迟系统的稳定性具有稳定的延迟脉冲，其中脉冲的时间延迟在两个连续的脉冲瞬间之间是灵活的。为了解决脉冲中的时间延迟项，提出了平均脉冲延迟（AID）的概念。利用平均脉冲间隔和AID的思想，我们针对具有平均延迟脉冲的时滞系统，提出了一些基于Lyapunov的指数稳定性准则，脉冲延迟满足建议的AID条件的地方。结果表明，脉冲时间延迟具有双重影响，即可能使稳定的系统不稳定或使不稳定的系统稳定。有趣的是，还表明，对于某些具有稳定延迟脉冲的稳定延迟系统，在某些条件下，无论连续动力中延迟的大小如何，都可以确保稳定性。此外，我们将理论结果应用于具有传输延迟和采样延迟的蔡氏电路的脉冲同步控制。最后，通过一些例子说明了所得结果的有效性。还表明，对于某些具有稳定延迟脉冲的稳定延迟系统，在某些条件下，无论连续动力中延迟的大小如何，都可以确保稳定性。此外，我们将理论结果应用于具有传输延迟和采样延迟的蔡氏电路的脉冲同步控制。最后，给出了一些例子来说明导出结果的有效性。还表明，对于某些具有稳定延迟脉冲的稳定延迟系统，在某些条件下，无论连续动力中延迟的大小如何，都可以确保稳定性。此外，我们将理论结果应用于具有传输延迟和采样延迟的蔡氏电路的脉冲同步控制。最后，给出了一些例子来说明导出结果的有效性。