We address the problem of bounding 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, and define the "average
communication" of an encoder to be the long-term fraction of
resource-consuming symbols over all symbol-streams the encoder
may emit.

This talk explores how the imposition of limits on an encoder's
bit-rate and average communication 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 average bit
rate, average communication, and the unstable eigenvalues of A.