  We present analytical and numerical studies of pinned superconducting states
of open-ended Josephson ladder arrays, neglecting inductances but taking edge
effects into account. Treating the edge effects perturbatively, we find
analytical approximations for three of these superconducting states -- the
no-vortex, fully-frustrated and single-vortex states -- as functions of the dc
bias current $I$ and the frustration $f$. Bifurcation theory is used to derive
formulas for the depinning currents and critical frustrations at which the
superconducting states disappear or lose dynamical stability as $I$ and $f$ are
varied. These results are combined to yield a zero-temperature stability
diagram of the system with respect to $I$ and $f$. To highlight the effects of
the edges, we compare this dynamical stability diagram to the thermodynamic
phase diagram for the infinite system where edges have been neglected. We
briefly indicate how to extend our methods to include self-inductances.
