The finite-time passivity problem is, respectively, investigated for stochastic coupled complex networks (SCCNs) with and without time-varying delay. Firstly, we present several new concepts about finite-time passivity in the sense of expectation on the basis of existing passivity definition. By designing appropriate controllers, the finite-time passivity of SCCNs with and without time-varying delay is obtained. In addition, the definition of finite-time synchronization in the sense of expectation is proposed. Under some sufficient conditions and designed controllers, finite-time passivity derives finite-time synchronization. Finally, two examples are given to demonstrate the effectiveness of finite-time passive and synchronization criteria.

中文翻译：

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随机耦合复杂网络的有限时间无源性

分别针对具有和不具有时变延迟的随机耦合复杂网络 (SCCN) 研究了有限时间无源问题。首先，我们在现有被动性定义的基础上，提出了期望意义上的有限时间被动性的几个新概念。通过设计合适的控制器，可以获得有和没有时变延迟的 SCCN 的有限时间无源性。此外，提出了期望意义上的有限时间同步的定义。在一些充分条件和设计好的控制器下，有限时间无源性推导出有限时间同步。最后，给出了两个例子来证明有限时间被动和同步准则的有效性。