On stabilizability of LTI systems across a Gaussian MAC channel

In this paper, the problem of stabilizing two scalar plants across a Gaussian multiple access channel (MAC) is addressed. Both states are encoded separately and sent across a shared MAC channel to a joint decoder/controller. A necessary condition for stabilizing such a system in the mean square sense is obtained using information-theoretic tools. This condition establishes the relationship between the magnitude of the unstable eigenvalues and the capacity region of Gaussian feedback multiple-access channel. A time-division encoding scheme along with a switched linear control law is proposed to achieve a rate region that is sufficient for stabilizability. The problem is studied both under the assumption that the two encoders can cooperate by sharing information and that they cannot.