Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays

Journal Article · Mon Sep 18 00:00:00 EDT 2017 · IEEE Transactions on Automatic Control

DOI:https://doi.org/10.1109/TAC.2017.2754219· OSTI ID:1438231

Meng, Ziyang ^[1]; Yang, Tao ^[2]; Li, Guoqi ^[1]; Ren, Wei ^[3]; Wu, Di ^[4]

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1. Tsinghua Univ., Beijing (China). Dept. of Precision Instrument
2. Univ. of North Texas, Denton, TX (United States). Electrical Engineering
3. Univ. of California, Riverside, CA (United States). Dept. of Electrical Engineering
4. Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Energy and Environment Directorate

Here, we study synchronization of coupled linear systems over networks with weak connectivity and nonuniform time-varying delays. We focus on the case where the internal dynamics are time-varying but non-expansive (stable dynamics with a quadratic Lyapunov function). Both uniformly jointly connected and infinitely jointly connected communication topologies are considered. A new concept of quadratic synchronization is introduced. We first show that global asymptotic quadratic synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of infinitely jointly connected communication topology. In particular, for the undirected communication topologies, it turns out that the existence of a uniform time interval for the jointly connected communication topology is not necessary and quadratic synchronization can be achieved when the time-varying nonuniform delays are arbitrarily bounded. Finally, simulation results are provided to validate the theoretical results.

• Research Organization: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE; National Natural Science Foundation of China (NSFC)
• Grant/Contract Number: AC05-76RL01830; 61503249; 4173075; 2016YFB0500902
• OSTI ID: 1438231
• Report Number(s): PNNL-SA-116223
• Journal Information: IEEE Transactions on Automatic Control, Vol. 63, Issue 6; ISSN 0018-9286
• Publisher: IEEE
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
Linear time-varying system
Synchronization
Switching topology
Time-varying nonuniform delay