  We illustrate a technique for specifying piecewise constant controls for
classes of switched electrical networks, typically used in converting power in
a dc-dc converter. This procedure makes use of decompositions of SU(2) to
obtain controls that are piecewise constant and can be constrained to be
bang-bang with values 0 or 1. Complete results are presented for a third order
network first. An example, which shows that the basic strategy is viable for
fourth order circuits, is also given. The former evolves on SO(3), while the
latter evolves on SO(4). Since the former group is intimately related to SU(2)
while the latter is related to SU(2)xSU(2), the methodology of this paper uses
factorizations of SU(2). The systems in this paper are single input systems
with drift. In this paper, no approximations or other artifices are used to
remove the drift. Instead, the drift is important in the determination of the
controls. Periodicity arguments are rarely used.
