March 3, 2026Open Access

An Auxiliary Function-Based Control Scheme for Stabilizing Fractional-Order Systems

Key Points

Global asymptotic stability is achieved through a novel control mechanism, enhancing stability methods.
The auxiliary function enables flexibility with the Lyapunov function, allowing stability conditions beyond traditional requirements.
Simulations of the Newton-Leipnik chaotic system validate the effectiveness of the proposed method in controlling such dynamics.
The proposed scheme may lead to advancements in controlling complex fractional-order chaotic systems.

Abstract

This work proposes a new scheme for stabilizing fractional-order systems (FOSs) in which we offer an auxiliary function such that the fractional derivative for the Lyapunov function candidate could be positive or negative, rather than the conventional negative definiteness condition required for stability. Such a foundation is employed to introduce a simple control mechanism that stabilizes the FOS at its zero equilibrium point and provides global asymptotic stability. To show the applicability of our method, we provide a numerical example supported by simulations of the Newton-Leipnik chaotic system, proving its ability to address complex fractional-order chaotic systems through a simple controller.

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Akbarian et al. (Wed,) studied this question.

synapsesocial.com/papers/69a75f01c6e9836116a2a155 https://doi.org/https://doi.org/10.1016/j.ifacol.2026.01.010

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