Control of Feedback Systems Subject to the Finite Rate Constraints via the Shannon Lower Bound

This paper is concerned with control of stochastic systems subject to limited feedback channel capacity. Specifically, the design of an encoder, decoder, and controller subject to the mean square observability and stabilizability is considered. It is shown that by transmitting information which is equal to the Shannon lower bound, mean square observability and stabilizability over Additive White Gaussian Noise (AWGN) channel is achieved. Furthermore, a modified definition for channel capacity and rate distortion is presented which is suitable for control applications and real time communication.