Synchronization of Lurie systems with quantized and triggered control under limited transmission capacity

In this paper, quantized and triggered control is utilized to sample output error signal for output feedback synchronization of two Lurie systems (formed by linear part and nonlinear one constructed only by the measurable output) under limited transmission capacity. With the characteristics of output error, we come up with practical quantized and triggered strategy to sample the output error instead of the traditional equal time sampling. Different from the existing trigger method, the proposed method fully utilizes the structure of quantizer and it combines quantization error and sampling error as a whole. It is thoroughly discussed that the potential Zeno behavior would not occur under the proposed method. In addition, transmission bit rate is also calculated and it can be maintained within an acceptable range. It is demonstrated by two chaotic Chua systems in the simulation that our method can not only meet required performance, but also save transmission resources.