Robust Guaranteed Synchronization for Chaotic Systems With Incremental Quadratic Constraints

This paper concerns the robust guaranteed synchronization of chaotic systems subject to unknown but amplitude-bounded parameter perturbation, process disturbance, and measurement noise. The incremental quadratic constraints are adopted to provide a unified description of chaotic systems, based on which a circle criterion-based observer with $\ell _{\infty }$ performance is design to attenuate the impacts of unknown uncertainties on synchronization error. Based on the designed observer, a zonotope-based guaranteed synchronization algorithm is proposed via mean value extension and zonotope inclusion techniques, where all the uncertainties from parameter perturbation, process disturbance, measurement noise, and chaotic behavior are taken into consideration. Finally, simulation results on the hyper-chaotic Chen system are presented to demonstrate the effectiveness of the proposed method.