A motivating example is given by sensors and actuators communicating over a wireless channel for which the quality of the communication link varies over time because of random fading in the received signal. In the case of digital communication, this can reflect in a time variation of the rate supported by the wireless channel. However, if the channel variations are slow enough, transmitter and receiver can estimate the quality of the link by sending a training sequence, and can adapt the communication scheme to the channel's condition.

We ask the following question is it possible to design a communication scheme that changes dynamically according to the channel's condition and, at the same time, is guaranteed to stabilize the system?

We answer the above in terms of a data rate theorem which relates the speed of the dynamics of the plant to the information-theoretic rate of the communication channel.

The theorem provides necessary and sufficient conditions for stabilization, and its implications and relationships with related results in the literature are discussed. Joint work with P. Minero, G. Nair, and S. Dey.