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M. Hovd and S. Skogestad

Automatica

**30** (6), pages 957-973

**Abstract**

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-&infty; 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&infty;-optimal control this also yields `super-optimality',
where the H&infty; 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 subproblems of the same dimension as the
subsystems. This leads to a dramatic reduction in dimension for systems
composed of many subsystems.