  This paper presents scalable controller synthesis methods for heterogeneous
and partially heterogeneous systems. First, heterogeneous systems composed of
different subsystems that are interconnected over a directed graph are
considered. Techniques from robust and gain-scheduled controller synthesis are
employed, in particular the full-block S-procedure, to deal with the
decentralized system part in a nominal condition and with the interconnection
part in a multiplier condition. Under some structural assumptions, we can
decompose the synthesis conditions into conditions that are the size of the
individual subsystems. To solve these decomposed synthesis conditions that are
coupled only over neighboring subsystems, we propose a distributed method based
on the alternating direction method of multipliers. It only requires
nearest-neighbor communication and no central coordination is needed. Then, a
new classification of systems is introduced that consists of groups of
homogeneous subsystems with different interconnection types. This
classification includes heterogeneous systems as the most general and
homogeneous systems as the most specific case. Based on this classification, we
show how the interconnected system model and the decomposed synthesis
conditions can be formulated in a more compact way. The computational
scalability of the presented methods with respect to a growing number of
subsystems and interconnections is analyzed, and the results are demonstrated
in numerical examples.
