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

• Published in: Applied mathematics and computation 2023-03, Vol.440, p.127668, Article 127668
• Main Authors: Xing, Ying, He, Xinyi, Li, Xiaodi
• Format: Article
• Language: English
• Subjects: Disturbance; Finite-time stability; Impulse sequence; Impulsive systems; Settling time
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127668

•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. What we concern in this paper is finite-time control of nonlinear impulsive systems involving external disturbance, where practical finite-time and finite-time stabilization are studied with respect to nonvanishing and vanishing disturbance, respectively. A relationship 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 settling time is also smaller. For the sake of illustrating the validity of proposed results, some examples and their simulations are provided.