Global finite-time synchronization for fractional complex network via impulsive control based on a new finite-time stability result

This paper focuses on the finite-time stability (FTS) issue for fractional nonlinear impulsive systems (FNISs). By applying Lyapunov functional approach and fractional calculus, a novel result with respect to the FTS is developed, where stabilizing impulse and destabilizing impulse are introduced in systems simultaneously. The settling time (ST), which is related to the impulse numbers, the impulse gain and the order of systems, is calculated accurately. Moreover, the proposed theoretical results are applied to derive the global finite-time synchronization (GFS) conditions for fractional-order complex dynamic network (FCDNs) under hybrid impulse effects. Finally, a simulation example is provided to substantiate the validity of the obtained results.