Prescribed-time stabilization of uncertain nonlinear impulsive systems with multiple delays

Ruyi Wang; Chunyan Zhang; Lichao Feng; Zhihui Wu; Ruyi Wang; Chunyan Zhang; Lichao Feng; Zhihui Wu

doi:10.3934/era.2025233

Electronic Research Archive

2025, Volume 33, Issue 9: 5207-5230. doi: 10.3934/era.2025233

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Research article

Prescribed-time stabilization of uncertain nonlinear impulsive systems with multiple delays

1.
College of Science, and Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China
2.
School of Automation, Harbin University of Science and Technology, Harbin 150080, China

Received: 07 July 2025 Revised: 16 August 2025 Accepted: 25 August 2025 Published: 02 September 2025

Researchers have reported on prescribed-time stability (PTS) for delay systems, but they do not take into account the significant impulses phenomenon and focus on only single delay. To tackle these two aspects, we aimed to investigate PTS issues for nonlinear impulsive systems with multiple time-varying delays and uncertainties. By the Lyapunov-Krasovskii functional method, PTS criteria were established for multi-delay systems. Specifically speaking, an adaptive control strategy was proposed for multi-delay systems to achieve PTS through the integrated design of time-varying delay compensation and uncertainty handling, which could ensure system states and control inputs to precisely converge to the origin within the prescribed time frame. Furthermore, the proposed method significantly enhanced the system's robustness against time-varying delays and uncertainties, thus overcoming the limitations of traditional methods in terms of convergence time and disturbance rejection capability. Finally, a simulation result was given to verify the feasibility and effectiveness of the proposed method.
- uncertain impulsive systems,
- multiple delays,
- Lyapunov-Krasovskii functional,
- prescribed time stability,
- settling time
Citation: Ruyi Wang, Chunyan Zhang, Lichao Feng, Zhihui Wu. Prescribed-time stabilization of uncertain nonlinear impulsive systems with multiple delays[J]. Electronic Research Archive, 2025, 33(9): 5207-5230. doi: 10.3934/era.2025233

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Abstract

Researchers have reported on prescribed-time stability (PTS) for delay systems, but they do not take into account the significant impulses phenomenon and focus on only single delay. To tackle these two aspects, we aimed to investigate PTS issues for nonlinear impulsive systems with multiple time-varying delays and uncertainties. By the Lyapunov-Krasovskii functional method, PTS criteria were established for multi-delay systems. Specifically speaking, an adaptive control strategy was proposed for multi-delay systems to achieve PTS through the integrated design of time-varying delay compensation and uncertainty handling, which could ensure system states and control inputs to precisely converge to the origin within the prescribed time frame. Furthermore, the proposed method significantly enhanced the system's robustness against time-varying delays and uncertainties, thus overcoming the limitations of traditional methods in terms of convergence time and disturbance rejection capability. Finally, a simulation result was given to verify the feasibility and effectiveness of the proposed method.

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