Based on a previously introduced framework for distributed controller synthesis, in this note a novel transformation of interconnectionmatrices is proposed that enables to consider arbitrary, time-varying and directed interaction topologies. It represents any interconnection as a virtual interconnection matrix that has the property of being normal, i.e., that guarantees the existence of a unitary diagonalizing transformation, which admits to decompose the synthesis problem in terms of the entire interconnected system into problems of subsystem scale, which can then be solved by standard convex multiplier-based gain-scheduling synthesis methods with complexity in the order of a single subsystem. When compared with a method from the literature, themethod shows superior performance in both a numerical example and the leader-follower formation control problem of nonlinear quadrocopter models.