  A control system is called self-powered if the only energy it requires for
operation is that which it absorbs from the plant. For a linear feedback law to
be feasible for a self-powered control system, its feedback signal must be
colocated with the control inputs, and its input-output mapping must satisfy an
associated passivity constraint. The imposition of such a feedback law can be
viewed equivalently as the imposition of a linear passive shunt admittance at
the actuation ports of the plant. In this paper we consider the use of
actively-controlled electronics to impose a self-powered linear feedback law.
To be feasible, it is insufficient that the imposed admittance be passive,
because parasitic losses must additionally be overcome. We derive sufficient
feasibility conditions which explicitly account for these losses. In the
finite-dimensional, time-invariant case, the feasibility condition distills to
a more conservative version of the Positive Real Lemma, which is parametrized
by various loss parameters. Three examples are given, in which this condition
is used to determine the least-efficient loss parameters necessary to realize a
desired feedback law.
