Observers-based synchronization and input recovery for a class of nonlinear chaotic models

In this paper, we propose a simple and efficient crypto-system based on a chaotic time delay model. It consists of two steps: the first one assures the transmitter/receiver synchronization while the second step focuses on the encryption/decryption procedure. The synchronization is performed through a non linear state observer design, driven by the transmitted signal. Both full order and reduced order state estimation techniques are established. One of the main results is that sufficient conditions for asymptotic convergence, to assure the synchronization, are derived in terms of linear matrix inequalities (i.e., convex problem) easily and numerically tractable. Efficiency of the proposed approach is shown through the transmission of two encrypted messages: a sound wave and a digital picture. Finally, some security issues are discussed at the end of this paper.