Abstract
This paper considers the control of a continuous-time linear time-invariant plant over a communication channel with limited capacity and zero transmission delay. The control goal is to guarantee containability while it is assumed that an event-based sampling mechanism is the only component in the control loop that is equipped with memory In particular, this implies that the usage of a dynamic controller is explicitly excluded. The main contribution of the paper is to affirmatively answer the question whether in such a static scenario, with event-based sampling it is still possible to guarantee containability with an arbitrarily small asymptotic average bit rate. To address this question, results from the field of time-optimal control for linear systems are used. Afterwards, the derivations are illustrated for a system with two unstable eigenvalues.
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