Transient response of minimum variance control over a Gaussian communication channel

Recently, a finite horizon minimum variance control problem was proposed using feedback over a Gaussian communication channel. Because only the terminal state is penalized, it was shown that linear communication and control strategies are optimal and achieve the information theoretic minimum cost. However, because the transient state is not penalized, the transient behavior can be poor. In the present paper, we show that if there is at most one open loop unstable plant pole, then the transient response will remain bounded as the control horizon tends to infinity, and will approach a value determined by the solution to a certain algebraic Riccati equation.