Abstract
The problems on synchronization and pinning control for complex dynamical networks with interval time‐varying delay are investigated and two less conservative criteria are established based on reciprocal convex technique. Pinning control strategies are designed to make the complex networks synchronized. Moreover, the problem of designing controllers can be converted into solving a series of NMIs (nonlinear matrix inequalities) and LMIs (linear matrix inequalities), which reduces the computation complexity when comparing with those present results. Finally, numerical simulations can verify the effectiveness of the derived methods.
Highlights
During the past decades, complex dynamical networks have increasingly become a focal research topic and received much attention in various fields such as physics, chemistry, and computer science 1–4
Suppose that the nodes are coupled with states xi ·, i ∈ {1, . . . , N}, the complex dynamical networks can be described by xi t f xi t g xi t − τ t li1j Exj t li2j Fxj t − τ t, 2.1
2.9 are asymptotically stable with respect to their zero solutions, the complex networks 2.1 can achieve the synchronization at s t, where J t Bf s t is the Jacobian matrix of f x t at s t, and Γ t Bg x t − τ t is the Jacobian matrix of g x t − τ t at s t − τ t
Summary
Complex dynamical networks have increasingly become a focal research topic and received much attention in various fields such as physics, chemistry, and computer science 1–4 Such systems in the real world usually consist of a large number of highly interconnected dynamical units. Some researchers have considered the global or robust or cluster synchronization for various coupled delayed neural networks based on some effective techniques including LMI one in 8–12. In , cluster synchronization for stochastic delayed neural networks was studied based on pinning control and LMI approach. With existence of various couplings, the synchronization has been analyzed for delayed complex networks using pinning adaptive control in. In , the authors have presented linear feedback and adaptive feedback pinning control to synchronize the delayed complex networks. XY ∗Z with ∗ denoting the symmetric term in a symmetric matrix
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