This paper is concerned with ${H}_{\infty }$ synchronization of coupled oscillators in a master–slave framework, in which the oscillators cannot be stabilized by nondelayed sampled position data, but can be stabilized by sampled position data with delays restricted by nonzero lower bounds and upper bounds. A configuration of networked master–slave oscillators with a remote controller is first constructed. Then the positive effects of delays on master–slave synchronization are investigated. Some delay-dependent ${H}_{\infty }$ synchronization criteria are derived by constructing augmented discretized Lyapunov–Krasovskii functionals for determinate sampling and stochastic sampling, respectively. The controller can be designed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to verify the theoretical results. It is shown that the maximum allowable sampling period in the case of stochastic sampling is larger than the one in the case of determinate sampling. Stochastic sampling can also provide a tradeoff between network-induced delays and the sampling periods, enhancing the master–slave synchronization performance.

中文翻译：

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带有延迟位置数据的网络主从振荡器的$H∞同步：网络引起的延迟的积极影响

本文关注的是 $ {H} _ {\ infty} $ 主从框架中耦合振荡器的同步，其中振荡器不能通过非延迟采样位置数据来稳定，但是可以通过采样位置数据来稳定，其时延受非零下限和上限限制。首先构造了带有遥控器的联网主从振荡器的配置。然后研究了延迟对主从同步的积极影响。一些依赖于延迟 $ {H} _ {\ infty} $ 通过构造分别用于确定采样和随机采样的增强离散Lyapunov-Krasovskii函数来导出同步标准。可以通过求解一组线性矩阵不等式来设计控制器。最后，通过两个数值例子验证了理论结果。结果表明，随机采样的最大允许采样周期大于确定采样的最大采样周期。随机采样还可以在网络引起的延迟和采样周期之间进行权衡，从而增强主从同步性能。