On stabilizability of Markov jump linear systems across a Gaussian parallel channel

The problem of feedback stabilization of discrete-time Markov jump linear systems (MJLS) over a Gaussian parallel channel is addressed. In this channel, the transmitter sends a common message to both receivers. A necessary condition for stabilizing MJLS in the mean square sense is obtained using information-theoretic methods. This condition establishes the relationship between the characteristics of MJLS and the parameters of Gaussian parallel channel. Finally, a numerical example is given to illustrate the proposed results.