  Relaxed conditions are given for stability of a feedback system consisting of
an exponentially stable multi-input multi-output nonlinear plant and an
integral controller. Roughly speaking, it is shown that if the composition of
the plant equilibrium input-output map and the integral feedback gain is
infinitesimally contracting, then the closed-loop system is exponentially
stable if the integral gain is sufficiently low. The main result is illustrated
with an application arising in frequency control of AC power systems. We
demonstrate how the contraction condition can be checked computationally via
semidefinite programming, and how integral gain matrices can be synthesized via
convex optimization to achieve robust L2 performance in the presence of
nonlinearity and uncertainty.
