This paper addresses the problem of asymptotic stabilization for linear time-invariant (LTI) systems using event-triggered control under finite data rate communication - both in the sense of finite precision data at each transmission and finite average data rate. Given a prescribed rate of convergence for asymptotic stability, we introduce an event-triggered control implementation that opportunistically determines the transmission instants and the finite precision data to be transmitted at each transmission. We show that our design exponentially stabilizes the origin while guaranteeing a positive lower bound on the inter-transmission times, ensuring that the number of bits transmitted at each transmission is upper bounded, and allowing for the possibility of transmitting fewer bits at any given time if more bits than prescribed were transmitted on a previous transmission. In our technical approach, we consider both the case of instantaneous and non-instantaneous transmissions. Several simulations illustrate the results.
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