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

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  • Assali, El Abed
  • Li, Ruiqi

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.

Suggested Citation

  • Assali, El Abed & Li, Ruiqi, 2025. "Laplace transform for a new adaptive predefined stability theorem and its application to the synchronization of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s096007792500791x
    DOI: 10.1016/j.chaos.2025.116778
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