Exponential input-to-state stability of nonlinear systems under impulsive disturbance via aperiodic intermittent control

Siyue Yao; Jin-E Zhang; Siyue Yao; Jin-E Zhang

doi:10.3934/math.2025490

AIMS Mathematics

2025, Volume 10, Issue 5: 10787-10805. doi: 10.3934/math.2025490

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Research article

Exponential input-to-state stability of nonlinear systems under impulsive disturbance via aperiodic intermittent control

Siyue Yao ,
Jin-E Zhang ^,

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

Received: 21 February 2025 Revised: 17 April 2025 Accepted: 30 April 2025 Published: 12 May 2025
MSC : 93C10, 93D40

In this paper, the exponential input-to-state stabilization (EISS) problem for nonlinear systems subject to impulsive disturbance and continuous external inputs is addressed by an aperiodic intermittent control (APIC), which is further classified as either time-triggered APIC (TAPIC) or event-triggered APIC (EAPIC). To establish sufficient conditions for the realization of EISS, the Lyapunov approach is used. It is shown that the suggested APIC can successfully reduce the negative consequences of continuous external inputs and impulsive disturbance. Limiting the percentage of the active interval in the control procedure yields a range of impulse moments under TAPIC. The relationship among impulse disturbance, intermittent control parameters, the event-triggered mechanism (ETM), and the threshold is established under EAPIC to guarantee EISS. The predesigned ETM is used to generate a series of impulse disturbance moments. Furthermore, the Zeno phenomenon is excluded. Finally, an example of Chua's oscillator is presented to show how effective the system is under TAPIC and EAPIC.
- impulse disturbance,
- aperiodic intermittent control,
- time-triggered and event-triggered,
- input-to-state stabilization
Citation: Siyue Yao, Jin-E Zhang. Exponential input-to-state stability of nonlinear systems under impulsive disturbance via aperiodic intermittent control[J]. AIMS Mathematics, 2025, 10(5): 10787-10805. doi: 10.3934/math.2025490

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Abstract

In this paper, the exponential input-to-state stabilization (EISS) problem for nonlinear systems subject to impulsive disturbance and continuous external inputs is addressed by an aperiodic intermittent control (APIC), which is further classified as either time-triggered APIC (TAPIC) or event-triggered APIC (EAPIC). To establish sufficient conditions for the realization of EISS, the Lyapunov approach is used. It is shown that the suggested APIC can successfully reduce the negative consequences of continuous external inputs and impulsive disturbance. Limiting the percentage of the active interval in the control procedure yields a range of impulse moments under TAPIC. The relationship among impulse disturbance, intermittent control parameters, the event-triggered mechanism (ETM), and the threshold is established under EAPIC to guarantee EISS. The predesigned ETM is used to generate a series of impulse disturbance moments. Furthermore, the Zeno phenomenon is excluded. Finally, an example of Chua's oscillator is presented to show how effective the system is under TAPIC and EAPIC.

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