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A convex characterization of classes of problems in control with specific interaction and communication structures

We present a list of optimal disturbance rejection problems in systems in which the overall control scheme is required to have a certain structure. These structures correspond to various classes of controlled systems which include what we refer to as nested, chained, hierarchical, delayed interaction and communication, and, symmetric systems. The common thread in all of these classes is that by taking an input-output point of view we can characterize all stabilizing controllers in terms of convex constraints in the Youla-Kucera parameter. The disturbance rejection problem can therefore be casted as a convex, yet nonstandard, model matching problem. Approaches that solve this problem are presented for various optimality criteria.