On the Synchronization of Bidirectionally Coupled Nonidentical Systems via Output Feedback

We investigate the synchronization of bidirectionally coupled nonidentical chaotic systems, addressing a critical challenge in nonlinear dynamics. Unlike traditional master-slave or unidirectional synchronization approaches, we propose a novel synchronization scheme based on output feedback linearization that ensures identical synchronization even in the presence of parameter mismatches and structural differences between systems. Our approach incorporates a nonlinear switching feedback law, which enhances stability and robustness in bidirectionally coupled configurations. We analyze the synchronization conditions using Lyapunov stability theory and illustrate our results through numerical simulations on well-known benchmark chaotic systems, including the Lorenz and Sprott systems. Our findings demonstrate that the proposed method can achieve stable synchronization in both identical and nonidentical configurations, even when the systems exhibit piecewise nonlinearities. These results extend the applicability of synchronization techniques to a broader class of chaotic systems and lay the groundwork for future research in networked dynamical systems.