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This paper deals with static output feedback Hinfin control of a class of discrete-time networked control systems (NCSs) subject to random failures and random delays. The different random processes are modeled as Markovian chains, and the resulting closed-loop system belongs to the class of discrete-time Markovian jump linear systems (MJLS). For synthesis purposes, we adopt a new framework, based on the synthesis of ellipsoidal sets of controllers. Results are formulated as matrix inequalities. A numerical algorithm based on nonconvex optimization is provided and its running is illustrated on a classical example from literature.