  This paper provides a method to analyze the small-signal L2 gain of
control-affine nonlinear systems on compact sets via iterative semi-definite
programs. First, a continuous piecewise affine storage function and the
corresponding upper bound on the L2 gain are found on a bounded, compact set's
triangulation. Then, to ensure that the state does not escape this set, a
barrier function is found that is robust to small-signal inputs. Small-signal
L2 stability then holds inside each sublevel set of the barrier function inside
the set where the storage function was found. The bound on the inputs is also
found while searching for a barrier function. The method's effectiveness is
shown in a numerical example.
