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On the infimal Signal-to-Noise Ratio limitations for measurable disturbance rejection

In networked control a channel model is explicitly considered in the classical control feedback configuration. This channel model can be located over the control path, between the controller and the plant, or over the feedback path, between the plant and the controller (or over both simultaneously). It has been shown that an important channel parameter for the stabilisability of the control feedback loop is the channel Signal-to-Noise Ratio (SNR). In this work we propose the controller design to satisfy a given user SNR requirement, when a feed-forward controller is also implemented to compensate the presence of a measurable disturbance. We then highlight the resulting trade-off between measurable disturbance rejection requirement and infimal SNR requirement for both, the control path and the feedback path locations.