Input-to-state stability of impulsive stochastic delayed systems under linear assumptions
Input-to-state stability of impulsive stochastic delayed systems under linear assumptions
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DOI：
10.1016/j.automatica.2016.01.002
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发表时间：
2016-04
期刊：
影响因子：
--
通讯作者：
Xiaotai Wu;Yang Tang;Wenbing Zhang
中科院分区：
文献类型：
--
作者：
Xiaotai Wu;Yang Tang;Wenbing Zhang
研究了脉冲随机时滞系统的输入-状态稳定性(ISS)、积分-ISS(IISS)和随机ISS(SISS)。利用Lyapunov-Krasovskii函数和平均脉冲区间方法，在线性假设下分别得到了脉冲失稳和稳定的ISS性质的条件。证明了：如果连续随机时滞系统是ISS，且脉冲效应是不稳定的，则关于平均脉冲区间的下界，混杂系统是ISS。此外，还揭示了如果连续随机时滞系统不是ISS，则脉冲效应可以使系统在给定的平均脉冲区间上界成功地镇定。针对脉冲随机时滞系统，提出了一种改进的比较原理，便于对ISS/IISS/SISS的结果进行推导。最后给出了一个网络控制系统的算例，说明了所提结果的有效性。
In this paper, the input-to-state stability (ISS), integral-ISS (iISS) and stochastic-ISS (SISS) are investigated for impulsive stochastic delayed systems. By means of the Lyapunov–Krasovskii function and the average impulsive interval approach, the conditions for ISS-type properties are derived under linear assumptions, respectively, for destabilizing and stabilizing impulses. It is shown that if the continuous stochastic delayed system is ISS and the impulsive effects are destabilizing, then the hybrid system is ISS with respect to a lower bound of the average impulsive interval. Moreover, it is unveiled that if the continuous stochastic delayed system is not ISS, the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval. An improved comparison principle is developed for impulsive stochastic delayed systems, which facilitates the derivations of our results for ISS/iISS/SISS. An example of networked control systems is provided to illustrate the effectiveness of the proposed results.