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

This paper shows that a large class of chaotic systems, introduced in [2, 3], as the generalized Lorenz system, can be used to systematically generate synchronized chaotic oscillations. For two coupled such 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 transmitter and any initial error. The technique used stems from ideas used in nonlinear control to design asymptotical observers. It is based on nonlinear coordinate transformation leading to the form having all its crucial nonlinearities depending on synchronizing signal only. The dependence on systems parameters, that may potentially serve as encryption "password", is analyzed as well, indicating an interesting potential for the possible encryption use. Both theoretical analysis and numerical simulations are given, thereas confirming the proposed design, methodology.