  Classical conditions for ensuring the robust stability of a linear system in
feedback with a sector-bounded nonlinearity include small gain, circle,
passivity, and conicity theorems. In this work, we present a similar stability
condition, but expressed in terms of relations defined on a general semi-inner
product space. This increased generality leads to a clean result that can be
specialized in a variety of ways. First, we show how to recover both sufficient
and necessary-and-sufficient versions of the aforementioned classical results.
Second, we show that suitably choosing the semi-inner product space leads to a
new necessary and sufficient condition for weighted stability, which is in turn
sufficient for exponential stability.
