Rate-limited control of systems with uncertain gain

Controlling and stabilizing systems involves countering the impact of explicit communication constraints in addition to inherent system model parameter uncertainty and random noise. Here we use an information-theoretic approach to jointly tackle all three issues and understand their interactions. Our main result bounds the minimum communication rate required for the mean-square stability of a system with uncertain system gain. Moreover, our techniques extend to provide a finer characterization of the required rate when specific finite bounds on the second moment of the state are desired.