We address the problem of bounding a continuous-time LTI process under
communication constraints. We assume that the sensor sends symbols
from a finite alphabet to the actuator over a finite-capacity
communication channel, and that one symbol from the alphabet consumes
no communication resources. This talk explores how the imposition of
limits on an encoder's bit-rate and average fraction of non-free
symbol transmissions affect the encoder/decoder/controller's ability
to keep the process bounded. We conclude with the construction of an
emulation-based controller and event-based encoder/decoder which are
straightforward to implement, bound the process, and use bit-rate and
average power within a constant factor of the optimal bound.