Abstract
In this paper, the problem of fixed-time outer synchronization over double-layered neuron-based networks with uncertain parameters in nonlinear nodes dynamics and delayed coupling among the nodes is studied. To solve the problem, we propose a delay-dependent controller. Via employing Lyapunov stability theory for the double-layered networks, some sufficient criteria for the fixed-time outer synchronization are provided. To guarantee that the uncertain parameters are identified, an adaptive update identification law is designed. The designed controllers and the sufficient criteria can be applied not only to fixed-time synchronization of double-layered directed networks, but also to fixed-time synchronization of double-layered undirected networks. Our results indicate that the fixed settling time is related to the designed controllers, the size for neuron-based networks, the number of uncertain parameters for each neuron and the dimension of each neuron node in the fixed-time synchronization. Simulation examples illustrating the results are included.
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