Quasi-synchronization of fractional-order multi-layer networks with mismatched parameters via delay-dependent impulsive feedback control.

The paper is devoted to investigating the quasi-synchronization issue of fractional-order multi-layer networks with mismatched parameters under delay-dependent impulsive feedback control. It is worth highlighting that fractional-order multi-layer networks with mismatched parameters, as the extension model for single-layer or two-layer ones, are constructed in this paper. Simultaneously, the intra-layer and inter-layer couplings are taken into consideration, which is more general and rarely considered in discussions of network synchronization. An extended fractional differential inequality with impulsive effects is given to establish the grounded framework and theory on the quasi-synchronization problem under delay-dependent impulsive feedback control. Moreover, in the light of the Lyapunov method and graph theory, two criteria for achieving the quasi-synchronization of fractional-order multi-layer networks with mismatched parameters are derived. Furthermore, exponential convergence rates as well as the bounds of quasi-synchronization errors are successfully deduced. Ultimately, the theoretical results are applied in a practical power system, and some illustrative examples are proposed to show the effectiveness of theoretical analysis.