We study and develop a robust control framework for malware filtering and network security. We investigate the malware filtering problem by capturing the tradeoff between increased security on one hand and continued usability of the network on the other. We analyze the problem using a linear control system model with a quadratic cost structure and develop algorithms based on H infinity-optimal control theory. A dynamic feedback filter is derived and shown via numerical analysis to be an improvement over various heuristic approaches to malware filtering. The results are verified and demonstrated with packet level simulations on the Ns-2 network simulator.