Event-triggered impulsive control for exponential stabilization of fractional-order differential system

Mohsen DLALA; Abdelhamid ZAIDI; Farida ALHARBI; Mohsen DLALA; Abdelhamid ZAIDI; Farida ALHARBI

doi:10.3934/math.2025741

AIMS Mathematics

2025, Volume 10, Issue 7: 16551-16569. doi: 10.3934/math.2025741

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Research article

Event-triggered impulsive control for exponential stabilization of fractional-order differential system

1.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
2.
Department of Mathematics and Physics, IPEIS, Sfax University, Tunisia
3.
Department of Computer Engineering and Mathematics, INSAT, Carthage University, Tunisia

Received: 19 May 2025 Revised: 16 June 2025 Accepted: 26 June 2025 Published: 22 July 2025
MSC : 26A33, 33C05, 33C20

This paper presents a novel event-triggered control strategy for fractional-order systems. The analysis begins with an investigation of the stability of impulsive fractional differential equations using Lyapunov function methods. Based on this framework, impulsive control schemes both with and without delay are designed to be triggered by discrete events. The proposed strategies ensure exponential stability of all system states while rigorously avoiding Zeno behavior. The effectiveness and practical relevance of the approach are demonstrated through numerical simulations applied to chaotic financial systems.
- fractional derivatives,
- Lyapunov functions,
- event-triggered impulsive control,
- exponential stabilization,
- financial chaotic systems
Citation: Mohsen DLALA, Abdelhamid ZAIDI, Farida ALHARBI. Event-triggered impulsive control for exponential stabilization of fractional-order differential system[J]. AIMS Mathematics, 2025, 10(7): 16551-16569. doi: 10.3934/math.2025741

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Abstract

This paper presents a novel event-triggered control strategy for fractional-order systems. The analysis begins with an investigation of the stability of impulsive fractional differential equations using Lyapunov function methods. Based on this framework, impulsive control schemes both with and without delay are designed to be triggered by discrete events. The proposed strategies ensure exponential stability of all system states while rigorously avoiding Zeno behavior. The effectiveness and practical relevance of the approach are demonstrated through numerical simulations applied to chaotic financial systems.

References

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