Exponential synchronization for multi-weighted dynamic networks via finite-level quantized control with adaptive scaling gain

In recent years, the application of quantized control to the synchronization issue in dynamic networks has aroused widespread interest due to its effectiveness in improving communication efficiency. However, most existing designs of quantized controllers demand an infinite amount of quantization levels, which may be infeasible in practice because of the high cost of control and the difficulty of actual implementation. This work aims to propose a finite-level quantized control scheme to cope with the exponential synchronization problem for multi-weighted dynamic networks (MWDNs). First, a cost-effective and easy-to-implement finite-level quantized control scheme is developed, and then a novel adaptive updated law is introduced to dynamically scale the synchronous error signals, to scale the out-of-range signals back to the quantization range. By using such control protocol and constructing a new Lyapunov function, a sufficient condition is established to ensure the exponential synchronization rather than quasi-synchronization in the addressed MWDNs. Meanwhile, the convergence rate is also explicitly estimated. Also, some quasi-synchronization criterion without scaling the synchronous error signals is given. Finally, a numerical example is provided to support our theoretical results.