This paper addresses the impulsive stabilization problem for a class of time-delay systems in the presence of input disturbances. A novel impulsive control law is constructed, which is based on the discrete-time equivalent control design technique. The sliding-mode-based impulsive control law allows counteracting the disturbance effect using its previous step value. To adapt in real time to the variation in sampling periods, the sliding function is designed as a function of impulse interval. Piecewise Lyapunov functions based on the partition on the maximum impulse interval are introduced to deal with the time-varying structure of the sliding function. Sufficient conditions for exponential input-to-state stability (EISS) of the impulsively controlled systems are derived, in which the EISS gain characterizes the attenuation ability of the proposed impulsive control law on the disturbance estimation error. The disturbance attenuation performance of the proposed impulsive control strategy is demonstrated through the time-delay Chua’s circuit.

中文翻译：

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一类输入扰动时滞系统的滑模脉冲控制

本文解决了存在输入干扰时一类时滞系统的脉冲稳定问题。基于离散时间等效控制设计技术，构造了一种新颖的脉冲控制律。基于滑模的脉冲控制律允许使用其先前的步长值来抵消干扰效应。为了实时适应采样周期的变化，滑动函数被设计为脉冲间隔的函数。引入基于最大脉冲区间划分的分段Lyapunov函数来处理滑动函数的时变结构。推导了脉冲控制系统指数输入状态稳定性（EISS）的充分条件，其中EISS增益表征了所提出的脉冲控制律对扰动估计误差的衰减能力。通过时滞蔡氏电路证明了所提出的脉冲控制策略的干扰衰减性能。