A practical projective synchronization approach for uncertain chaotic systems with dead-zone input

In this paper, a practical projective synchronization problem of master–slave chaotic systems is investigated. More specifically, a fuzzy adaptive slave chaotic system subject to dead-zone nonlinearity in the input channel is proposed using only the measurable output of the master system thanks to a suitable observer. A practical projective synchronization between the master and slave systems is achieved by an adequate fuzzy adaptive control system. The underlying parameter adaptation design as well as stability analysis are carried out using a Lyapunov based approach. Unlike the previous works, in the design of the proposed synchronization scheme, we do not require to know the uncertainties function and that the dynamics of the original synchronization error are strictly positive real (SPR). In fact, herein, the uncertainties function is estimated by a fuzzy adaptive system and the dynamics of the original synchronization error are augmented by a low pass filter designed to satisfy the SPR condition. Simulation results are given to show the effectiveness of the proposed practical projective synchronization scheme.