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In this paper, the robust (weighted) H _∞ filtering and feedback control problems are considered in the case of time variant and time invariant uncertainties. Using a separation of graph theorem with the scalings/multipliers approach, solutions to these problems can be proposed as an infinite dimensional convex optimization problem. The main result is to prove that in both cases and for both problems, both infinite dimensional convex optimization problems can be converted into finite dimensional convex optimization problem involving linear matrix inequality (LMI) constraints which is an extension of previously published results of Giusto and Paganini (1999)