  This paper presents a novel anti-windup proportional-integral controller for
stable multi-input multi-output nonlinear plants. We use tools from projected
dynamical systems theory to force the integrator state to remain in a desired
(compact and convex) region, such that the plant input steady-state values
satisfy the operational constraints of the problem. Under suitable monotonicity
assumptions on the plant steady-state input-output map, we use singular
perturbation theory results to prove the existence of a sufficiently small
controller gain ensuring closed-loop (local) exponential stability and
reference tracking for a feasible set of constant references. We suggest a
particular controller design, which embeds (when possible) the right inverse of
the plant steady-state input-output map. The relevance of the proposed
controller scheme is validated through an application in the power systems
domain, namely, the output (active and reactive) power regulation for a
grid-connected synchronverter.
