A new framework for robust observer-based synchronization of chaotic systems with a delay-aware LQR controller

Synchronizing chaotic systems is a fundamental challenge with significant applications, yet its practical implementation is often hindered by non-ideal channel characteristics such as noise and time delay. This paper introduces a new, robust framework for achieving high-fidelity synchronization in such challenging environments. The primary objective is to develop and validate a control strategy that is resilient to both limited state information and realistic channel imperfections. Our methodology pairs a Luenberger-style state observer with a novel, delay-aware Linear-Quadratic Regulator (LQR) within a master–slave system configuration. The controller explicitly compensates for input delay using a formulation derived from Lyapunov–Krasovskii theory and demonstrates the efficacy of actuating on a single, strategically selected state variable. Simulations conducted over a high-fidelity fiber-optic channel model confirm the framework’s performance. The results demonstrate rapid, precise synchronization that is robust to significant time-varying delays (up to 28ms), achieving settling times as low as 0.8 s while maintaining a steady-state error on the order of 10−5 amidst signal noise and quantization effects. The observer-based partial-state feedback approach successfully matches the performance of full-state feedback, validating its effectiveness. This work presents a comprehensive solution that significantly enhances the feasibility of applying chaos synchronization in real-world systems, proving its stability and robustness against a wide range of initial conditions and channel disturbances.