In this paper, a novel distributed guaranteed cost congestion control (DGCC) strategy for mobile networks with differentiated services traffic is developed. The switching or changes in the network topologies is modeled by a Markovian process. By incorporating communication capability among controllers, the distributed congestion controller is shown to be in fact equivalent to a local state feedback control plus a nearest neighboring controllers' adjustment with proportional gains. Numerical simulation results are presented to illustrate the effectiveness and capabilities of our proposed DGCC strategies.