Quantized hybrid impulsive control for finite-time synchronization of fractional-order uncertain multiplex networks with multiple time-varying delays

In this paper, the finite-time synchronization (FTS) problem of fractional-order multiplex networks with internal delay, intra- and inter-layer coupling delays, and uncertain intra- and inter-layer coupling matrices is studied. A new hybrid controller, composed of an impulsive controller and a quantized controller, is designed to achieve FTS for the considered network in order to save control resources and reduce the burden of the network. Based on the fractional-order Lyapunov function method, utilizing the fractional-order impulsive finite-time inequality and other inequality methods, several fresh sufficient conditions for the synchronization of the fractional-order uncertain multiplex network (FOUMN) with multiple time-varying delays in an explicitly estimated finite time are obtained. These sufficient criteria also reflect that the FTS of the network is related to its topology, quantization parameters, the order of the fractional derivative, and the impulse function. Lastly, two numerical examples confirm that the theoretical findings are valid.