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.

Automated summary

This paper focuses on finite-time control of nonlinear impulsive systems with external disturbance. It studies practical finite-time and finite-time stabilization for nonvanishing and vanishing disturbance, respectively. The relationship between finite settling time and impulsive frequency is presented to show the stabilizing effect of impulses. The results demonstrate that systems under nonvanishing disturbance can reach a disturbance-dependent ultimate bound in finite-time, and stabilizing impulses can lead to a relatively smaller settling time. Additionally, systems subject to vanishing disturbance can achieve finite-time stabilization at the origin, with a smaller settling time compared to the situation without impulses. Examples and simulations are provided to validate the proposed results.