Sampled-data nonlinear observer design for chaos synchronization: A Lyapunov-based approach

•A sampled-data observer-based chaos synchronization scheme is proposed for a large class of continuous-time and discrete-time chaotic systems.•Lyapunov-like theorems are employed to give sufficient conditions for exponential boundedness of estimation error in the presence of measurement noise.•Semiglobal and global convergence of estimation error is guaranteed unlike most of existing methods such as extended Kalman filter which provide local results.•To optimize the upper bound on estimation error, a suboptimal LMI criterion is derived.

This paper considers sampled-data based chaos synchronization using observers in the presence of measurement noise for a large class of chaotic systems. We study discretized model of chaotic systems which are perturbed by white noise and employ Lyapunov-like theorems to come up with a simple yet effective observer design. For the choice of observer gain, a suboptimal criterion is obtained in terms of LMI. We present semiglobal as well as global results. The proposed scheme can also be extended for discrete-time chaotic systems. Numerical simulations have been carried out to verify the effectiveness of theoretical results.