  This technical note investigates the minimum average transmit power required
for mean-square stabilization of a discrete-time linear process across a
time-varying additive white Gaussian noise (AWGN) fading channel that is
presented between the sensor and the controller. We assume channel state
information at both the transmitter and the receiver, and allow the transmit
power to vary with the channel state to obtain the minimum required average
transmit power via optimal power adaptation. We consider both the case of
independent and identically distributed fading and fading subject to a Markov
chain. Based on the proposed necessary and sufficient conditions for
mean-square stabilization, we show that the minimum average transmit power to
ensure stabilizability can be obtained by solving a geometric program.
