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Aperiodically intermittent stabilization for complex-valued hybrid stochastic delayed systems: An average technique
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2021-04-19 , DOI: 10.1016/j.cnsns.2021.105852
Pengfei Wang , Shaoyu Li , Huan Su

This paper focuses on the stabilization problem of complex-valued hybrid stochastic delayed systems via aperiodically intermittent control (AIC). As for AIC in existing literature, strict conditions on the lower bound of control intervals and upper bound of control periods or the maximum proportion of rest intervals are required. In this paper, we relax these constraints by proposing average control ratio and average control period to describe the distribution of control and rest intervals of AIC, i.e., the lower bound of certain control widths can be arbitrarily small, upper bound of certain control periods can be very large and the proportion of rest widths can be any value in (0,1). Thus, the conservativeness is reduced compared with the existing related results. Then based on the complex generalized Itô’s formula, several novel stabilization criteria are obtained for small time delays and large time delays, respectively, which avoid splitting the real and imaginary parts. Especially, for the case of small time delays, the upper bound of time delays can be larger than the lower bound of all control widths, which has wider applications than previous results. Finally, two examples along with their numerical simulations are given to show the effectiveness and less conservativeness of our results.



中文翻译:

复值混合随机时滞系统的非周期性间歇镇定:一种平均技术

本文着重研究非周期间歇控制(AIC)对复值混合随机时滞系统的镇定问题。对于现有文献中的AIC,要求对控制间隔的下限和控制周期的上限或休息间隔的最大比例的严格条件。在本文中,我们通过提出平均控制比和平均控制周期来描述AIC的控制和休息间隔的分布,从而放松了这些约束,即,某些控制宽度的下限可以任意小,某些控制周期的上限可以很大,其余宽度的比例可以是01个。因此,与现有的相关结果相比,保守性降低了。然后,基于复杂的广义Itô公式,分别针对较小的时延和较大的时延获得了几种新颖的稳定准则,这些准则避免了将实部和虚部分开。特别是,对于较小的时间延迟,时间延迟的上限可以大于所有控制宽度的下限,这比以前的结果具有更广泛的应用。最后,给出了两个例子及其数值模拟,以证明我们的结果的有效性和较小的保守性。

更新日期:2021-05-08
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