Mean square stabilizability of a Markov jump linear system Using Gaussian relay communication channels is investigated. Firstly, necessary conditions of general Gaussian channels are given to guarantee the mean square stabilizability of the Markov jump linear system. Considering two specified types of Gaussian relay channels (i.e. half-duplex cascade channels and nonorthogonal network channels) with average power constraint, the relationships between mean square stabilizability of the Markov jump linear system and the parameters of the communition channels are presented. Finally, the proposed theoretic results ars verified by a numerical example.□