This paper is concerned with control of plants composed of n similar interacting subsystems. Such plants are common in practice and include paper machines, distribution networks, coating processes, and plants consisting of units operating in parallel. The transfer function matrices for these systems are block symmetric circulant. For H(infinity) and H-2-optimal control, controller synthesis is simplified by considering n/2 + 1 independent problems of dimension n times smaller than the original problem. For the case of H(infinity)-optimal control this also yields ’super-optimality’, where the H(infinity) criterion is optimized in n directions, and not only in the worst direction. If the offdiagonal blocks (’interactions’) are identical the matrix is termed block parallel, and controller synthesis involves only two independent sub-problems of the same dimension as the subsystems. This leads to a dramatic reduction in dimension for systems composed of many subsystems.