The stability and stabilization problems for a class of stochastic Markov jump systems are investigated. The
systems under consideration are more general, since transition probabilities of the mode jumps can be partly unknown,
which includes the systems with completely known and completely unknown transition probabilities as two special cases.
Firstly, the sufficient condition for the stochastic Markov jump systems to be asymptotically mean square stable is derived,
and the state feedback stabilization controller is designed. Then, the design of the static output feedback controller is
presented based on singular value decomposition of matrices, and the design problem can be reduced to a set of linear
matrix inequalities(LMIs) feasibility problem. Finally, a numerical example shows the effectiveness of the obtained results.