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

Abstract

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.

Authors:
 [1];  [2];  [1];  [3];  [4]
  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
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE; National Natural Science Foundation of China (NNSFC)
OSTI Identifier:
1438231
Report Number(s):
PNNL-SA-116223
Journal ID: ISSN 0018-9286
Grant/Contract Number:
AC05-76RL01830; 61503249; 4173075; 2016YFB0500902
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
IEEE Transactions on Automatic Control
Additional Journal Information:
Journal Name: IEEE Transactions on Automatic Control; Journal ID: ISSN 0018-9286
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Linear time-varying system; Synchronization; Switching topology; Time-varying nonuniform delay

Citation Formats

Meng, Ziyang, Yang, Tao, Li, Guoqi, Ren, Wei, and Wu, Di. Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays. United States: N. p., 2017. 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 Time-Varying Delays. United States. doi:10.1109/TAC.2017.2754219.
Meng, Ziyang, Yang, Tao, Li, Guoqi, Ren, Wei, and Wu, Di. Mon . "Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying Delays". United States. doi:10.1109/TAC.2017.2754219.
@article{osti_1438231,
title = {Synchronization of Coupled Dynamical Systems: Tolerance to Weak Connectivity and Arbitrarily Bounded Time-Varying 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 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.},
doi = {10.1109/TAC.2017.2754219},
journal = {IEEE Transactions on Automatic Control},
number = ,
volume = ,
place = {United States},
year = {Mon Sep 18 00:00:00 EDT 2017},
month = {Mon Sep 18 00:00:00 EDT 2017}
}

Journal Article:
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