Synchronization design of chaotic systems via robust state observers

The synchronization design problem via a robust state observer in a class of nonlinear feedback chaotic systems with a disturbance signal is studied in this paper. Based on the parametric solutions of a Sylvester matrix equation, the considered synchronization design problem in chaotic systems is changed into an optimal problem with some constraints. By solving the optimal problem, the gain matrix of the robust state observer in the synchronization design is obtained, which can make the disturbance decouple from the output. Finally, a numerical example and its simulation results show the simplicity and effectiveness of the proposed synchronization design method via a robust state observer in chaotic systems.