In this paper, a novel congestion control strategy for mobile networks with differentiated services traffic is proposed. The switching or changes in the network topology is modeled by a Markovian process. By utilizing the guaranteed cost control approach, a maximum bound on the jump quadratic cost function is guaranteed for each traffic class with respect to its specific QoS requirements. The proposed Markovian jump guaranteed cost congestion controller (MJ-GCC) is shown to be robust to the unknown and time-varying network delays and the non-stationary network topologies. Numerical simulation results are presented to illustrate the effectiveness and capabilities of our proposed MJ-GCC strategies.