  In this paper, we consider the problem of second moment stabilization of a
scalar linear plant with process noise. We assume that the sensor must
communicate with the controller over an unreliable channel, whose state evolves
according to a Markov chain, with the transition matrix on a timestep depending
on whether there is a transmission or not on that timestep. Under such a
setting, we propose an event-triggered transmission policy which meets the
objective of exponential convergence of the second moment of the plant state to
an ultimate bound. Furthermore, we provide upper bounds on the transmission
fraction of the proposed policy. The guarantees on performance and transmission
fraction are verified using simulations.
