Synchronization of a class of chaotic systems via a nonlinear observer approach

This paper shows that a large class of chaotic systems, introduced as a generalized Lorenz system, can be used to systematically generate synchronized chaotic oscillations. For two coupled 3-dimensional oscillators, only a scalar channel connection is needed for achieving chaotic synchronization. Moreover, the suggested synchronization is globally exponentially convergent for any signal of the transmitter and any initial error. The technique used stems from ideas used in the nonlinear control to design asymptotical observers. It is based on the nonlinear coordinate transformation leading to the form having all its crucial nonlinearities depending on the synchronizing signal only. The dependence on systems parameters, that may potentially serve as encryption "password", is also analyzed, indicating an interesting potential for the possible encryption use. Both the theoretical analysis and numerical simulations are given confirming the effectiveness of the proposed design methodology.