The DOI matches its Crossref record; 47 of the 47 references it cites were found in a registry or an index.
Finite-Time and Fixed-Time Cluster Synchronization With or Without Pinning Control
Abstract
In this paper, the finite-time and fixed-time cluster synchronization problem for complex networks with or without pinning control are discussed. Finite-time (or fixed-time) synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time, and the settling time depends on the initial values for finite-time synchronization (or the settling time is bounded by a constant for any initial values for fixed-time synchronization). To realize the finite-time and fixed-time cluster synchronization, some simple distributed protocols with or without pinning control are designed and the effectiveness is rigorously proved. Several sufficient criteria are also obtained to clarify the effects of coupling terms for finite-time and fixed-time cluster synchronization. Especially, when the cluster number is one, the cluster synchronization becomes the complete synchronization problem; when the network has only one node, the coupling term between nodes will disappear, and the synchronization problem becomes the simplest master-slave case, which also includes the stability problem for nonlinear systems like neural networks. All these cases are also discussed. Finally, numerical simulations are presented to demonstrate the correctness of obtained theoretical results.
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Cites
Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788
Finite-Time Stability of Continuous Autonomous Systems
Bhat, S. P., & Bernstein, D. S. (2000) · SIAM Journal on Control and Optimization · doi:10.1137/s0363012997321358 · Cited by 5,510
Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems
Polyakov, A. (2012) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2011.2179869 · Cited by 5,207
Continuous finite-time stabilization of the translational and rotational double integrators
Bhat, S. P., & Bernstein, D. S. (1998) · IEEE Transactions on Automatic Control · doi:10.1109/9.668834 · Cited by 1,694
Finite-Time Consensus Problems for Networks of Dynamic Agents
Wang, L., & Xiao, F. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2041610 · Cited by 1,170
Finite-time and fixed-time stabilization: Implicit Lyapunov function approach
Polyakov, A., Efimov, D., & Perruquetti, W. (2015) · Automatica · doi:10.1016/j.automatica.2014.10.082 · Cited by 972
Finite-time formation control for multi-agent systems
Xiao, F., Wang, L., Chen, J., & Gao, Y. (2009) · Automatica · doi:10.1016/j.automatica.2009.07.012 · Cited by 934
Haimo, V. T. (1986) · SIAM Journal on Control and Optimization · doi:10.1137/0324047 · Cited by 920
Finite-time convergent gradient flows with applications to network consensus
Cortés, J. (2006) · Automatica · doi:10.1016/j.automatica.2006.06.015 · Cited by 818
Distributed robust finite-time nonlinear consensus protocols for multi-agent systems
Zuo, Z., & Tie, L. (2016) · International Journal of Systems Science · doi:10.1080/00207721.2014.925608 · Cited by 797
Metadata
- Authors
- Liu, X., & Chen, T.
- Venue
- IEEE Transactions on Cybernetics
- Published
- 2018-01
- Volume
- 48
- Issue
- 1
- Pages
- 240-252
- ISSN
- 2168-2267 (ISSN-L)
- 2168-2275
- OpenAlex
- W2560040317
- Cited by
- 287
- References
- 47
- FWCI
- 20.21
- Type
- journal article
- Language
- en
- Open access
- closed
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