Self-triggered delay impulsive control for nonlinear systems with exogenous disturbances

Biwen Li; Yuan Cai; Biwen Li; Yuan Cai

doi:10.3934/math.2026330

AIMS Mathematics

2026, Volume 11, Issue 3: 8014-8030. doi: 10.3934/math.2026330

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Research article

Self-triggered delay impulsive control for nonlinear systems with exogenous disturbances

Biwen Li ,
Yuan Cai ^,

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received: 24 January 2026 Revised: 01 March 2026 Accepted: 16 March 2026 Published: 26 March 2026
MSC : 93C30

This paper investigates input-to-state practical stability (ISpS) for a class of nonlinear dynamic systems subject to time-delayed impulsive effects and external inputs under self-triggered impulsive control (STIC). The considered framework features distinct external disturbances affecting both the continuous dynamics and the impulsive dynamics, with flexible delay characteristics associated with the impulses. To address the challenge of Zeno behavior, a self-triggering mechanism (STM) is proposed that dynamically determines impulse instants based on the combined information of the system state and external disturbances. By employing Lyapunov-based methods, sufficient conditions ensuring ISpS are derived. The theoretical results are further illustrated through an application example, where both the STM and the control gains are designed via matrix inequalities. Finally, two numerical examples are provided to demonstrate the validity and effectiveness of the proposed approach.
- input-to-state stability (ISS),
- nonlinear systems,
- self-triggered impulsive control,
- delayed impulsive,
- Zeno behavior
Citation: Biwen Li, Yuan Cai. Self-triggered delay impulsive control for nonlinear systems with exogenous disturbances[J]. AIMS Mathematics, 2026, 11(3): 8014-8030. doi: 10.3934/math.2026330

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Abstract

This paper investigates input-to-state practical stability (ISpS) for a class of nonlinear dynamic systems subject to time-delayed impulsive effects and external inputs under self-triggered impulsive control (STIC). The considered framework features distinct external disturbances affecting both the continuous dynamics and the impulsive dynamics, with flexible delay characteristics associated with the impulses. To address the challenge of Zeno behavior, a self-triggering mechanism (STM) is proposed that dynamically determines impulse instants based on the combined information of the system state and external disturbances. By employing Lyapunov-based methods, sufficient conditions ensuring ISpS are derived. The theoretical results are further illustrated through an application example, where both the STM and the control gains are designed via matrix inequalities. Finally, two numerical examples are provided to demonstrate the validity and effectiveness of the proposed approach.

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