In this paper, two novel congestion control strategies for mobile networks with differentiated services (Diff-Serv) traffic are presented, namely (i) a Markovian jump decentralized guaranteed cost congestion control strategy, and (ii) a Markovian jump distributed guaranteed cost congestion control strategy. The switchings or changes in the network topology are modeled by a Markovian jump process. By utilizing guaranteed cost control principles, the proposed congestion control schemes do indeed take into account the associated physical network resource constraints and are shown to be robust to unknown and time-varying network latencies and time delays. A set of Linear Matrix Inequality (LMI) conditions are obtained to guarantee the QoS of the Diff-Serv traffic with a guaranteed upper bound cost. Simulation results are presented to illustrate the effectiveness and capabilities of our proposed strategies. Comparisons with centralized and other relevant works in the literature focused on Diff-Serv traffic and mobile networks are also provided to demonstrate the advantages of our proposed solutions. (C) 2014 Elsevier Ltd. All rights reserved.