Impulsive control of nonlinear delay systems is studied in this paper, where the time delays addressed may be the constant delay, bounded time-varying delay, or unbounded time-varying delay. Based on the impulsive control theory and some analysis techniques, a new theoretical result for global exponential stability is derived from the impulsive control point of view. The significance of the presented result is that the stability can be achieved via the impulsive control at certain impulse points despite the existence of impulsive perturbations which causes negative effect to the control. That is, the impulsive control provides a super performance to allow the existence of impulsive perturbations. In addition, we apply the theoretical result to the problem of impulsive control of delayed neural networks. Some results for global exponential stability and synchronization control of neural networks with time delays are derived via impulsive control. Three illustrated examples are given to show the effectiveness and distinctiveness of the proposed impulsive control schemes.

中文翻译：

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时变时滞非线性系统的脉冲控制及应用


本文研究了非线性时滞系统的脉冲控制，所处理的时滞可以是恒定时滞、有界时变时滞或无界时变时滞。基于脉冲控制理论和一些分析技术，从脉冲控制的角度导出了全局指数稳定性的新理论结果。该结果的意义在于，尽管存在对控制造成负面影响的脉冲扰动，但可以通过在某些脉冲点处的脉冲控制来实现稳定性。也就是说，脉冲控制提供了允许脉冲扰动存在的超性能。此外，我们将理论结果应用于延迟神经网络的脉冲控制问题。通过脉冲控制得出了具有时滞的神经网络的全局指数稳定性和同步控制的一些结果。给出了三个示例来说明所提出的脉冲控制方案的有效性和独特性。