This article investigates the synchronization problem of interconnected linear two-time-scale systems (TTSSs) with switching topology. By utilizing the Chang transformation, a distributed synchronization protocol is proposed with event-triggered communication. Static and dynamic event-triggered mechanisms are proposed successively, which both contain two separated event-triggering conditions corresponding to the slow and the fast subsystems. The existence of a strictly positive time period between any two successive transmissions is ensured regardless of the initial states. The main difficulty of this study lies in that the state jump and parametric uncertainty appear because of the system transformation. To overcome the difficulty, the system is first modeled as an uncertain hybrid system. Then, the control gain is properly designed by solving Riccati-like equations dependent on the rough bounds of the eigenvalues of communication graph Laplacians, and a piecewise quadratic Lyapunov function is proposed with which the jump caused by the switching topology is subtly evaluated. Sufficient conditions are thus established to achieve the event-triggered synchronization. Furthermore, the results are also extended to solve the synchronization problem of the interconnected impulsive linear TTSSs. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

中文翻译：

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具有开关拓扑的互连线性双时标系统的分布式事件触发同步。

本文研究了具有开关拓扑的互连线性双时标系统 (TTSS) 的同步问题。利用Chang变换，提出了一种事件触发通信的分布式同步协议。相继提出了静态和动态事件触发机制，它们都包含两个独立的事件触发条件，分别对应于慢子系统和快子系统。无论初始状态如何，都确保在任何两个连续传输之间存在严格的正时间段。本研究的主要难点在于由于系统变换而出现状态跳跃和参数不确定性。为了克服这个困难，系统首先被建模为一个不确定的混合系统。然后，通过求解依赖于通信图拉普拉斯算子特征值粗界的Riccati-like 方程来适当设计控制增益，并提出分段二次Lyapunov 函数，巧妙地评估由开关拓扑引起的跳跃。这样就建立了实现事件触发同步的充分条件。此外，结果还扩展到解决互连脉冲线性 TTSS 的同步问题。最后，提供了三个数值例子来证明所提出的理论结果的有效性。这样就建立了实现事件触发同步的充分条件。此外，结果还扩展到解决互连脉冲线性 TTSS 的同步问题。最后，提供了三个数值例子来证明所提出的理论结果的有效性。这样就建立了实现事件触发同步的充分条件。此外，结果还扩展到解决互连脉冲线性 TTSS 的同步问题。最后，提供了三个数值例子来证明所提出的理论结果的有效性。