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Exponential synchronization of weighted general delay coupled and non-delay coupled dynamical networks. (English) Zbl 1205.93124
Summary: Time delays commonly exist in the real world. In the present work, we investigate the exponential synchronization of weighted general delay coupled and non-delay coupled complex dynamical networks with different topological structures. Based on the Lyapunov stability theory, the suitable controllers are designed to make the controlled dynamical network exponentially synchronize an isolated node with any pre-specified exponential convergence rate, and proved theoretically. The synchronization scheme is applicable to the undirected networks as well as the directed ones. The derived controllers are simple and can be readily used in practical applications. Furthermore, the coupling matrix is not necessary to be irreducible and the network node dynamics need not satisfy the very strong and conservative uniform Lipschitz condition. Numerical simulations further validate the effectiveness and feasibility of our synchronization method.
MSC:
93D15Stabilization of systems by feedback
37N35Dynamical systems in control
93C23Systems governed by functional-differential equations
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