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

Ying Xing, Xinyi He and Xiaodi Li

Applied Mathematics and Computation, 2023, vol. 440, issue C

Abstract: 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.

Keywords: Finite-time stability; Disturbance; Impulse sequence; Impulsive systems; Settling time (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007366

DOI: 10.1016/j.amc.2022.127668

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