  This paper deals with the stabilization of linear systems with process noise
under packet drops between the sensor and the controller. Our aim is to ensure
exponential convergence of the second moment of the plant state to a given
bound in finite time. Motivated by considerations about the efficient use of
the available resources, we adopt an event-triggering approach to design the
transmission policy. In our design, the sensor's decision to transmit or not
the state to the controller is based on an online evaluation of the future
satisfaction of the control objective. The resulting event-triggering policy is
hence specifically tailored to the control objective. We formally establish
that the proposed event-triggering policy meets the desired objective and
quantify its efficiency by providing an upper bound on the fraction of expected
number of transmissions in an infinite time interval. Simulations for scalar
and vector systems illustrate the results.
