Performance limitations in the control of LTI plants over fading channels

This paper presents performance limitations in the control of single-input linear time-invariant (LTI) plants when controlled over a fading channel. Our main result is a closed form characterization of the minimal stationary plant output variance, as an explicit function of channel statistics and plant characteristics. To derive our results, we first show that there exists an equivalence, in a second order moment sense, between a fading channel and an additive white noise channel subject to a stationary SNR constraint. Such equivalence is then exploited to state conditions for stabilization, and to derive explicit performance limitations, as immediate corollaries of known results in the literature on networked control subject to SNR constraints.