Control with minimum communication cost per symbol

We address the problem of stabilizing a continuous-time linear time-invariant process under communication constraints. We assume that the sensor that measures the state is connected to the actuator through a finite capacity communication channel over which an encoder at the sensor sends symbols from a finite alphabet to a decoder at the actuator. We consider a situation where one symbol from the alphabet consumes no communication resources, whereas each of the others consumes one unit of communication resources to transmit. This paper explores how the imposition of limits on an encoder´s bit-rate and average resource consumption affect the encoder/decoder/controller´s ability to keep the process bounded. The main result is a necessary and sufficient condition for a bounding encoder/decoder/controller which depends on the encoder´s bit-rate, its average resource consumption, and the unstable eigenvalues of the process.