Power spectral analysis of networked control systems with data dropouts

This note derives a closed-form expression for a control systemʹs 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 regulatorʹs 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.