Distributed Event-Triggered Synchronization of Interconnected Linear Two-Time-Scale Systems With Switching Topology
研究了具有切换拓扑的互联线性双时间尺度系统的同步问题，提出了基于事件触发通信的分布式同步协议，并设计了静态和动态事件触发机制，确保任意两次传输间存在严格正的时间间隔。
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.