  We consider control of multiple stable first-order \review{agents} which have
a control coupling described by an M-matrix. These agents are subject to
incremental sector-bounded \review{input} nonlinearities. We show that such
plants can be globally asymptotically stabilized to a unique equilibrium using
fully decentralized proportional-integral controllers equipped with anti-windup
and subject to local tuning rules. In addition, we show that when the
nonlinearities correspond to the saturation function, the closed loop
asymptotically minimizes a weighted 1-norm of the agents state mismatch. The
control strategy is finally compared to other state-of-the-art controllers on a
numerical district heating example.
