  The problem of late time instability in time domain integral equations for
electromagnetics is longstanding. While several techniques have been suggested
for addressing this problem, they either require impractically high degrees of
freedom in the basis function or an analytical computation of matrix elements.
The authors recently proposed a method that demonstrates stability without
requiring either of these. The paper, however, does not present theoretical
foundations for the choice of, or a rigorous error bounds on the approximation
of, the bilinear form. This paper complements the authors' previous work by
presenting a construction of the bilinear form based on the minimization of the
energy in the system and a proof for the bounds on the approximation. We
present results on the bounds developed and few sample scattering results that
demonstrate the stability of the proposed scheme.
