Laplace transform for a new adaptive predefined stability theorem and its application to the synchronization of chaotic systems

El Abed Assali and Ruiqi Li

Chaos, Solitons & Fractals, 2025, vol. 199, issue P2

Abstract: This paper presents a new adaptive predefined stability theorem using the Laplace transform and inequality techniques. Based on this theorem, we propose a new Lyapunov function and a sliding mode control method, with sufficient conditions for predefined-time synchronization. Additionally, an adaptive controller is introduced to ensure that the sliding mode surface is reached within a predefined time, even with uncertainties and external disturbances in chaotic systems. Finally, numerical simulations demonstrate that the proposed method achieves synchronization between an integer-order Chen and Lorenz systems within 2 s, with the sliding mode surface reached in 1 s and the synchronization error in 1 s, independent of the initial conditions. The controller performs well under bounded disturbances and model uncertainties. Compared to existing fixed-time control schemes, the proposed approach features a simpler structure, fewer controller parameters and improved robustness.

Keywords: Predefined-time stability; Sliding mode control; Chaotic synchronization; Drive–response systems; Chaotic systems (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s096007792500791x

DOI: 10.1016/j.chaos.2025.116778

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