Networked and quantized control systems with communication delays

There are many communication imperfections in networked control systems (NCSs) such as varying sampling/transmission intervals, varying delays, possible packet loss, communication constraints and quantization effects. Most of the available literature on NCSs focuses on only some of these phenomena, while ignoring the others, although recently some papers appeared that consider at least three of these phenomena. In one paper time-varying delays, time-varying transmission intervals and communication constraints are considered, while in an other time-varying transmission intervals, communication constraints and quantization effects are studied. As both approaches are based on the same underlying hybrid modeling framework, it will be shown here that the models can be combined in a unifying hybrid model including the five mentioned network phenomena under some restrictions. On the basis of this model, stability will be analyzed of the closed-loop system in which the controller is obtained using an emulation approach. The analysis provides tradeoffs between the maximally allowable transmission interval (MATI), the maximally allowable delay (MAD) and the quantization parameters, while still guaranteeing closed-loop stability.