Abstract: | In this paper we present an alternative solution to the problem min X ε Hn×n∞ |A + BXC|∞ where A, B, rmand C are rational matrices in Hn×n∞. The solution circumvents the need to extract the matrix inner factors of B and C, providing a multivariable extension of Sarason's H∞-interpolation theory 1] to the case of matrix-valued B(s) and C(s). The result has application to the diagonally-scaled optimization problem int |D(A + BXC)D−1|∞, where the infimum is over D, X εHn×n∞, D diagonal. |