Frequency-domain analysis of control loops with intermittent data losses

In this technical note, we propose a frequency-domain analysis framework for control systems with data losses, assumed to be statistically independent over time. Based on our framework, the amplitudes of the mean and variance of the output response to a sinusoidal input can be plotted as a function of the input frequency, much like in the classical Bode plot. Analogously to the classical analysis, this plot can be used for inferring the behavior of the output response, characterized now by its mean and variance, to an arbitrary input signal.