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On the Effect of Sampled-Data Hold and Discretization in Signal-to-Noise Ratio Constrained Control

Networked Control Systems (NCSs) involve some kind of communication network within feedback loops. One of the research topics that have arisen from the consideration of NCSs is that of the minimum data rate required to stabilize a given LTI plant. Data-rate limitations may be expressed in the form of signal-to-noise ratio (SNR) constraints. Existing results have characterized minimum data rates required for stabilization of continuous-time as well as discrete-time systems. However, the effect of sampled-data hold functions on the minimum data rate required for stabilization of a continuous-time system with a discrete-time controller has not yet received sufficient attention. In this paper, we show that, as far as SNR-constrained control is concerned, the use of zero-order hold may be preferable to first-order hold on first- or second-order plants with delay. We thus provide a result on the effect of sampled-data hold functions when the sampling period is given. As a second contribution, we analyze the effect of employing an approximate discrete-time representation on minimum data rates for stabilization.