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.
Highlights
Most real systems in nature, society and engineering can be properly described by models of complex networks of interacting dynamical units with diverse topologies [1]
Since the first observation of synchronization phenomenon of two pendulum clocks by Huygens in 1665, this phenomenon has been discovered in many biological and physical systems, such as pacemaker cells in the heart and nervous systems, synchronously flashing fireflies, networks of neurons in the circadian pacemaker [2,3]. Another topic that is closely related to the synchronization of complex networks is the consensus of multi-agent systems, which means that a team of agents reaches an agreement on certain quantities of interest through local communication
We will focus on the outer synchronization problem of two coupled fractional-order complex networks with the drive-response coupling structure, in which the drive network does not receive any information from the response network
Summary
Most real systems in nature, society and engineering can be properly described by models of complex networks of interacting dynamical units with diverse topologies [1]. In [39], the authors treated outer synchronization problem between two different bidirectionally coupled FCNs. the stability condition in that work depends on the eigenvalues of a large system matrix. Whether outer synchronization behavior between two FCNs can be achieved globally still remains an open problem, which motivates the research of this work Another motivation comes from concerns on controller gain variations. Using the stability theory of fractional-order systems and the characteristics of the eigenvalue distribution of Kronecker sum of two matrices, we present a basic theorem for outer synchronization Based on this basic theorem, two sufficient conditions for outer synchronization in the LMI format are derived for the additive and multiplicative controller gain perturbations, respectively. For A ∈ Rm×n and B ∈ Rp×q , A ⊗ B ∈ Rmn×pq denotes the Kronecker product of the two matrices
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