Lyapunov stability of nonlinear systems with impulsive disturbances and delayed impulses via event-triggered impulsive control

Xinyu Wu; Tongfei Xiao; Jin-E Zhang; Xinyu Wu; Tongfei Xiao; Jin-E Zhang

doi:10.3934/math.2026436

AIMS Mathematics

2026, Volume 11, Issue 4: 10589-10610. doi: 10.3934/math.2026436

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Research article

Lyapunov stability of nonlinear systems with impulsive disturbances and delayed impulses via event-triggered impulsive control

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

Received: 13 February 2026 Revised: 09 April 2026 Accepted: 10 April 2026 Published: 17 April 2026
MSC : 93C10

In this research, we used an event-triggered impulsive control (ETIC) approach to study the Lyapunov stability of nonlinear systems subject to impulsive disturbances and impulse delays. Based on impulsive control theory, a novel event-triggering mechanism (ETM) that incorporates impulsive disturbance information was developed. The proposed ETM adopts an intermittent monitoring scheme, under which the impulsive control instants are autonomously dictated, ensuring that the controller is activated exactly once between two consecutive impulsive perturbations. As a result, the divergent dynamic behaviors induced by disturbances can be rapidly and effectively restrained. Furthermore, sufficient conditions were derived to exclude the occurrence of Zeno behavior and to guarantee the global asymptotic stability (GAS) of the closed-loop system under the ETIC framework. In addition, by utilizing linear matrix inequality (LMI) techniques, the synchronization of chaotic systems was successfully achieved. Theoretical analysis revealed that the stability of the system depends not only on the designed ETM but also on the presence of impulse delays. Finally, two numerical simulation examples were provided to demonstrate the effectiveness and feasibility of the proposed approach.
- Lyapunov stability,
- delay impulsive systems,
- Zeno behavior,
- impulsive disturbance,
- event-triggered impulsive control
Citation: Xinyu Wu, Tongfei Xiao, Jin-E Zhang. Lyapunov stability of nonlinear systems with impulsive disturbances and delayed impulses via event-triggered impulsive control[J]. AIMS Mathematics, 2026, 11(4): 10589-10610. doi: 10.3934/math.2026436

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Abstract

In this research, we used an event-triggered impulsive control (ETIC) approach to study the Lyapunov stability of nonlinear systems subject to impulsive disturbances and impulse delays. Based on impulsive control theory, a novel event-triggering mechanism (ETM) that incorporates impulsive disturbance information was developed. The proposed ETM adopts an intermittent monitoring scheme, under which the impulsive control instants are autonomously dictated, ensuring that the controller is activated exactly once between two consecutive impulsive perturbations. As a result, the divergent dynamic behaviors induced by disturbances can be rapidly and effectively restrained. Furthermore, sufficient conditions were derived to exclude the occurrence of Zeno behavior and to guarantee the global asymptotic stability (GAS) of the closed-loop system under the ETIC framework. In addition, by utilizing linear matrix inequality (LMI) techniques, the synchronization of chaotic systems was successfully achieved. Theoretical analysis revealed that the stability of the system depends not only on the designed ETM but also on the presence of impulse delays. Finally, two numerical simulation examples were provided to demonstrate the effectiveness and feasibility of the proposed approach.

References

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