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We develop convex conditions that are necessary and sufficient for the existence of a controller that yields a closed loop that achieves consensus. The conditions generate controllers with no particular communication structure, but with optimal /spl Hscr//sub 2/ performance on the non-consensus part of the closed loop. We further explore the conditions to impose topology on the interconnection structure generated by the controllers. This is achieved by restricting a certain Lyapunov matrix to be block diagonal, in order to produce convex synthesis results.