This paper deals with the robustness stabilizability of the class of linear systems with markovian jumping parameters and unknown but bounded uncertainties. Under the assumption of the complete access to the system's states and its modes, we establish the robust stabilizability result under norm bounded uncertainties. Under the structured uncertainties, we will give the conditions under which the class of uncertain linear systems with jumping parameters remains stable. We also present a method of estimating the difference between the cost for the real system and the optimal performance for the nominal model. Our estimation result is independent of the uncertainties and is practically computable.