A feasible control design method is proposed for plants with discrete-time Markov jump parameters such that practical specifications and constraints are satisfied. It is assumed that the Markov chain is not measured. The concept of feasible control is applied to compute a discrete-time linear optimal controller structure such that both time-domain and frequency-domain constraints are satisfied. The controller is parametrised by a diagonal state weighting matrix Q. A standard mathematical programming algorithm is used to compute the state weighting matrix Q such that the specifications are met. The synthesis procedure consists of the iterative solution of an equation where at each iteration step a discrete-time linear optimal control problem is solved.