SNR limitation for amplitude-bounded noise in control over channels with feedback

This paper shows a limitation of signal-to-noise ratio (SNR) for amplitude-bounded noise in control of linear discrete-time systems over channels with feedback. The SNR allowed in stabilizing the closed-loop system is shown to depend on the product of unstable poles of the plant. The control law for minimizing the SNR is constructed from state-feedback controller and two observers employed in the data transmission and reception processes. The gain applied to the data to be transmitted is determined from the solution of a Riccati equation in minimum energy control depending on the observer gain. Moreover, we can observe in the case of SISO plants that lack of feedback for communication does not degrade the SNR limitation when the feedback for control is available in communication.