  We study local (also referred to as small-signal) stability of a network of
identical DC/AC converters having a rotating degree of freedom. We develop a
stability theory for a class of partitioned linear systems with symmetries that
has natural links to classical stability theories of interconnected systems. We
find stability conditions descending from a particular Lyapunov function
involving an oblique projection onto the complement of the synchronous steady
state set and enjoying insightful structural properties. Our sufficient and
explicit stability conditions can be evaluated in a fully decentralized
fashion, reflect a parametric dependence on the converter's steady-state
variables, and can be one-to-one generalized to other types of systems
exhibiting the same behavior, such as synchronous machines. Our conditions
demand for sufficient reactive power support and resistive damping. These
requirements are well aligned with practitioners' insights.
