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.