## AbstractWe 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. |

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