Fuzzy adaptive observer-based projective synchronization for nonlinear systems with input nonlinearity

In this paper, a projective synchronization problem of master-slave chaotic systems is investigated. More specifically, a fuzzy adaptive slave chaotic system subject to both sector nonlinearities and dead-zone in the input channel is proposed using only the measurable output of the master system thanks to a suitable observer. The asymptotical projective synchronization between the master and slave systems is achieved by an adequate fuzzy adaptive variable-structure control system. The underlying parameter adaptation design as well as the asymptotical synchronization and stability analysis are carried out using a Lyapunov based approach. The distinctive feature of the control design is that the uncertainties function and the gain reduction tolerances of the dead-zone are no longer required to be known thanks to the parameter adaptation capability of the control system. The proposed synchronization scheme is extended to two classes of the master-slave chaotic systems with time-delays. By using the Lyapunov-Krasovskii approach, some stability conditions relating to these classes are derived. Simulation results are given to show the effectiveness of the proposed projective synchronization scheme.