Power Spectral Analysis of Networked Control Systems With Data Dropouts

This note derives a closed-form expression for a control system's output power spectral density (PSD) as a function of the data dropout probability. We use the PSD to determine a dropout compensator that minimizes the regulator's output power. We show, by example, that the optimal dropout compensator does not always correspond to a filter that minimizes the mean square error between the predicted and dropped feedback measurement.