Invariant subspace technique for anti-windup synthesis

We discuss anti-windup synthesis for linear systems with input saturation. In particular, we discuss algorithms that induce an invariant subspace for the dynamic behavior of the mismatch between the constrained and unconstrained closed-loops. The dynamics in this invariant subspace are identical to the behavior of the plant with input saturation starting at the origin, stabilized by linear state feedback and driven by the mismatch between the unconstrained input and this input passed through a saturation function. In the static case, the state feedback gains are determined from a finite (perhaps empty) set of gains that are completely determined by the nominal controller. In the dynamic case, the state feedback gains are free design parameters.