This paper deals with the robustness of the class of discrete time linear systems with markovian jumping parameters and unknown but bounded uncertainties. Under the assumption that the markovian jump process (disturbance) is irreducible and the complete access to the system's state and its mode, we establish the necessary and sufficient conditions of stochastic stability for the autonomous nominal model. We also establish the sufficient condition for the robust stability result for this class of uncertain systems under matching conditions and the robust stability result under bounded uncertainties.