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In this paper, we investigate the regulation problem for linear discrete-time delay systems with Markovian jumps and constrained control. The constraints used here are of non symmetrical inequality type. A sufficient condition of stochastic stability of a closed loop system is derived. We use the positive invariance approach of the common set for all the modes to guarantee the admissibility of the control law. In the case of one mode, we obtain the condition of stability for a linear discrete-time delay system as known in the literature. A numerical example is given to illustrate the theoretic results.