Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded TimeVarying Delays
Here, we study synchronization of coupled linear systems over networks with weak connectivity and nonuniform timevarying delays. We focus on the case where the internal dynamics are timevarying but nonexpansive (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 timevarying nonuniform delays are arbitrarily bounded. Finally, simulation results are provided to validate the theoretical results.
 Authors:

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 Tsinghua Univ., Beijing (China). Dept. of Precision Instrument
 Univ. of North Texas, Denton, TX (United States). Electrical Engineering
 Univ. of California, Riverside, CA (United States). Dept. of Electrical Engineering
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Energy and Environment Directorate
 Publication Date:
 Report Number(s):
 PNNLSA116223
Journal ID: ISSN 00189286
 Grant/Contract Number:
 AC0576RL01830; 61503249; 4173075; 2016YFB0500902
 Type:
 Accepted Manuscript
 Journal Name:
 IEEE Transactions on Automatic Control
 Additional Journal Information:
 Journal Volume: 63; Journal Issue: 6; Journal ID: ISSN 00189286
 Publisher:
 IEEE
 Research Org:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org:
 USDOE; National Natural Science Foundation of China (NNSFC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; Linear timevarying system; Synchronization; Switching topology; Timevarying nonuniform delay
 OSTI Identifier:
 1438231
Meng, Ziyang, Yang, Tao, Li, Guoqi, Ren, Wei, and Wu, Di. Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded TimeVarying Delays. United States: N. p.,
Web. doi:10.1109/TAC.2017.2754219.
Meng, Ziyang, Yang, Tao, Li, Guoqi, Ren, Wei, & Wu, Di. Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded TimeVarying Delays. United States. doi:10.1109/TAC.2017.2754219.
Meng, Ziyang, Yang, Tao, Li, Guoqi, Ren, Wei, and Wu, Di. 2017.
"Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded TimeVarying Delays". United States.
doi:10.1109/TAC.2017.2754219. https://www.osti.gov/servlets/purl/1438231.
@article{osti_1438231,
title = {Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded TimeVarying Delays},
author = {Meng, Ziyang and Yang, Tao and Li, Guoqi and Ren, Wei and Wu, Di},
abstractNote = {Here, we study synchronization of coupled linear systems over networks with weak connectivity and nonuniform timevarying delays. We focus on the case where the internal dynamics are timevarying but nonexpansive (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 timevarying nonuniform delays are arbitrarily bounded. Finally, simulation results are provided to validate the theoretical results.},
doi = {10.1109/TAC.2017.2754219},
journal = {IEEE Transactions on Automatic Control},
number = 6,
volume = 63,
place = {United States},
year = {2017},
month = {9}
}