Modeling quantized fading channels as uncertainty: A quasi-Signal-to-Noise-Ratio approach

In this paper, we propose a new approach to model the network communication channel broadly used in networked control systems, which normally carries a quantizer subject to multiplicative random noise (fading effect). This new modeling approach is robust control oriented which allows factorization of the quantized fading channels (QFC) into a disturbance path, involving both quantization and fading impacts, and a nominal dedicated path. A quasi-Signal-to-Noise-Ratio (qSNR) is introduced to characterize the QFC, mimicking the traditional characterization of a disturbance uncertainty set in the norm bound. Through an example, it is shown that this new modeling approach turns the stabilizing control problem for networked systems with QFC into a normal small-gain design issue and offers a nice physical interpretation of the communication channel when its impact is considered on the performance of networked control systems. It is also shown that this new channel model is comprehensive, providing an unified expression of QFCs with either relative-error or multiplicative-error quantization.