Adaptive synchronization of chaotic systems with hysteresis quantizer input

This paper proposes two new designing methods of adaptive controllers in order to synchronize uncertain nonlinear chaotic systems with input quantization. The hysteresis quantizer, which is a class of sector-bounded quantizers, has been used to quantize the control signal. This can avoid the possible chattering caused by some conventional controllers. Two adaptive robust schemes are proposed to accomplish chaos synchronization of master and slave systems in presence of unknown parameters and uncertainties. The proposed controllers in this paper do not require the restrictive conditions for quantized parameters in contrast to some available control techniques for systems with input quantization. In addition, asymptotic stability of the proposed adaptive controllers is also verified analytically. Finally, the proposed controller is applied to a chaotic gyroscope and also to a Micro-Electro-Mechanical-System to validate its efficiency and robustness.