This paper considers the synchronization between two chaotic systems (i.e. master and slave systems) in the presence of practical constraints. The considered constraints are: the unavailability of state variables of both master and slave system, the presence of non-symmetric input saturation, model uncertainties and/or external disturbances (matched and/or unmatched). Considering these constraints, an adaptive robust observer-based controller is designed, which guarantees synchronization between the chaotic systems. For this purpose, a theorem is given and, according to a Lyapunov adaptive stabilization approach, it is proved that the robust synchronization via the proposed observer-based controller is guaranteed in the presence of actuator saturation and it is shown that even if the control signal is saturated, the proposed controller leads to a robust synchronization objective. Finally, in order to show the applicability of the proposed controller, it is applied on the Van der Pol chaotic systems. Computer simulations verify the theoretical results and show the effective performance of the proposed controller.
