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

## Abstract

We study synchronization of coupled linear systems over networks with weak connectivity and time-varying delays. We focus on the case that the internal dynamics are time-varying but non-expansive. Both uniformly connected and infinitely connected communication topologies are considered. A new concept of P-synchronization is introduced and we first show that global asymptotic P-synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of the 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 communication topology is not necessary and P-synchronization can be achieved when the time varying delays are arbitrarily bounded. Simulations are given to validate the theoretical results.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1440613

- Report Number(s):
- PNNL-SA-116223

Journal ID: ISSN 0018-9286

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: IEEE Transactions on Automatic Control; Journal Volume: 63; Journal Issue: 6

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Linear time-varying system; Synchronization; Switching topology; Time-varying 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., 2018.
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. Fri .
"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_1440613,
```

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 = {We study synchronization of coupled linear systems over networks with weak connectivity and time-varying delays. We focus on the case that the internal dynamics are time-varying but non-expansive. Both uniformly connected and infinitely connected communication topologies are considered. A new concept of P-synchronization is introduced and we first show that global asymptotic P-synchronization can be achieved over directed networks with uniform joint connectivity and arbitrarily bounded delays. We then study the case of the 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 communication topology is not necessary and P-synchronization can be achieved when the time varying delays are arbitrarily bounded. Simulations are given 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 = {Fri Jun 01 00:00:00 EDT 2018},

month = {Fri Jun 01 00:00:00 EDT 2018}

}