Minimal-Information Chaos Synchronization of the Lü System via Single-State Feedback Control
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Abstract
This study presents a low-complexity chaos synchronization strategy for the Lü system based on a minimal single-state feedback mechanism. A master–slave configuration is considered, where synchronization is achieved by transmitting only one state variable from the master system to the slave system. Unlike many existing approaches that rely on full-state information or a priori knowledge of state bounds, the proposed controller is constructed using a simple linear feedback law derived from cascade system stability theory. A Lyapunov-based analysis is employed to establish sufficient conditions for global asymptotic synchronization, ensuring rigorous theoretical justification. Numerical experiments conducted using the classical fourth-order Runge–Kutta method confirm the effectiveness of the proposed scheme and demonstrate rapid convergence of synchronization errors from arbitrary initial conditions. Due to its reduced information requirement and modest computational burden, the proposed method provides a practical and efficient framework for real-world chaotic synchronization applications.
Manuscript received: 30 Jan 2026 | Revised: 27 Mac 2026 | Accepted: 29 Apr 2026 | Published: 31 Jul 2026
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