Abstract—This paper explores the stabilization of the three-dimensional Fractional-Order (FO) chaotic Lorenz-84 atmosphere model through control strategies. Employing the Grünwald-Letnikov approximation for fractional integration, the chaotic system is simulated to understand its intricate dynamics. The main focus lies in utilizing state-space feedback control to adapt input signals based on system states, aiming to steer chaotic dynamics towards stability. Additionally, control gains optimization is conducted through Particle Swarm Optimization (PSO) to guarantee robust stabilization of the chaotic atmosphere model.

Keywords—Lorenz-84 Atmosphere model, chaotic system, fractional-order system, fractional integrator, Particle Swarm Optimization (PSO)

Cite: Nasr-Eddine Mellah, Sakina Benrabah, Samir Ladaci, "Fractional-Order Chaotic Lorenz-84 Atmosphere System Stabilization Using a Feedback State Space Control," International Journal of Applied Physics and Mathematics, vol. 15, no. 1, pp. 69-77, 2025.

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