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This paper discusses the use of networks-on-chip (NoCs) consisting of multiple voltage-frequency islands to cope with power consumption, clock distribution and parameter variation problems in future multiprocessor systems-on-chip (MPSoCs). In this architecture, communication within each island is synchronous, while communication across different islands is achieved via mixed-clock mixed-voltage queues. In order to dynamically control the speed of each domain in the presence of parameter and workload variations, we propose a robust feedback control methodology. Towards this end, we first develop a state-space model based on the utilization of the inter-domain queues. Then, we identify the theoretical conditions under which the network is controllable. Finally, we synthesize state feedback controllers to cope with workload variations and minimize power consumption. Experimental results demonstrate robustness to parameter variations and more than 40% energy savings by exploiting workload variations through dynamic voltage-frequency scaling (DVFS) for a hardware MPEG-2 encoder design.