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Entropy 2013, 15(4), 1357-1374; doi:10.3390/e15041357

Outer Synchronization between Fractional-Order Complex Networks: A Non-Fragile Observer-based Control Scheme

1
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China
2
Cisco School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Received: 25 February 2013 / Revised: 4 April 2013 / Accepted: 8 April 2013 / Published: 15 April 2013
(This article belongs to the Special Issue Dynamical Systems)
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Abstract

This paper addresses the global outer synchronization problem between two fractional-order complex networks coupled in a drive-response configuration. In particular, for a given fractional-order complex network composed of Lur’e systems, an observer-type response network with non-fragile output feedback controllers is constructed. Both additive and multiplicative uncertainties that perturb the control gain matrices are considered. Then, using the stability theory of fractional-order systems and eigenvalue distribution of the Kronecker sum of matrices, we establish some sufficient conditions for global outer synchronization. Interestingly, the developed results are cast in the format of linear matrix inequalities (LMIs), which can be efficiently solved via the MATLAB LMI Control Toolbox. Finally, numerical simulations on fractional-order networks with nearest-neighbor and small-world topologies are given to support the theoretical analysis.
Keywords: outer synchronization; fractional-order derivative; complex network; observer control; LMI outer synchronization; fractional-order derivative; complex network; observer control; LMI
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Zhao, M.; Wang, J. Outer Synchronization between Fractional-Order Complex Networks: A Non-Fragile Observer-based Control Scheme. Entropy 2013, 15, 1357-1374.

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