Stabilization of Markov jump linear systems over Gaussian relay channel

This paper deals with the problem of mean square (MS) stabilization for a Markov jump linear system (MJLS) over Gaussian relay channel subject to average power constraint. Based on the theory of entropy, a necessary condition of channel capacity for MS stabilization is proposed. Then by using the Schalkwijk-Kailath encoding scheme, a sufficient condition of MS stabilization is derived for a scalar MJLS. Finally, a numerical example is given to show the show the effectiveness and correctness of the theoretical work.