Lyapunov conditions for finite-time stability of disturbed nonlinear impulsive systems

•The problems of finite-time stabilization for nonlinear impulsive systems subject to nonvanishing and vanishing disturbances are investigated in this paper.•The relationship among the external disturbances, impulsive frequency and the system structure is established. Stabilizing effects of impulses are effectively utilized to deal with the instability caused by external disturbances.•Our results extend the practical finite-time stability and finite-time stability of continuous-time systems to impulsive systems.