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

What we concern in this paper is finite-time control of nonlinear impulsive systems in-volving external disturbance, where practical finite-time and finite-time stabilization are studied with respect to nonvanishing and vanishing disturbance, respectively. A relation-ship between the finite settling time and the impulsive frequency is presented to show the stabilizing effect of impulses. It is shown that systems subject to nonvanishing disturbance can enter a disturbance-dependent ultimate bound in a finite-time sense, and a relatively smaller bound of settling time is obtained by utilizing stabilizing impulses. Meanwhile, systems subject to vanishing disturbance can achieve finite-time stabilization at the origin. Moreover, compared with the situation without impulses, the corresponding bound of set-tling time is also smaller. For the sake of illustrating the validity of proposed results, some examples and their simulations are provided.(c) 2022 Elsevier Inc. All rights reserved.