Performance limits in the control of single‐input linear time‐invariant plants over fading channels

This study presents performance limitations in the control of single‐input linear time‐invariant plants when controlled over a fading channel. The authors consider two architectures where the controller is co‐located with the sensors. In the first architecture, the authors assume that delayed controller to actuator channel state information is available at the controller. In the second architecture, the authors relax that assumption and thus no channel‐state‐information is exploited at the controller. The authors’ main result is a closed form expression for the minimal stationary plant output variance, which is achievable in each scenario, as an explicit function of channel statistics and plant characteristics. To derive our results, the authors first show that there exists an equivalence, in a second‐order moment sense, between communication over a single fading channel and communication over an additive white noise channel subject to a stationary signal‐to‐noise ratio (SNR) constraint. Such equivalence is then exploited to state conditions for stabilisation, and to derive explicit performance limitations, as simple corollaries of known results in the literature on networked control subject to SNR constraints. Numerical examples are included to illustrate our findings.