Using the lumped circuit equations, we derive a stability criterion for
superconducting pinned states in two-dimensional arrays of Josephson junctions.
The analysis neglects quantum, thermal, and inductive effects, but allows
disordered junctions, arbitrary network connectivity, and arbitrary spatial
patterns of applied magnetic flux and DC current injection. We prove that a
pinned state is linearly stable if and only if its corresponding stiffness
matrix is positive definite. This algebraic condition can be used to predict
the critical current and frustration at which depinning occurs.Comment: To appear in Phys. Rev.
