The l2 anti-windup problem for discrete-time linear systems: definition and solutions

The anti-windup problem for discrete-time linear systems is formalized in terms of the l₂ norm of the deviation of the actual response of the system with saturation and anti-windup compensation from the (ideal) unconstrained response. We show that, paralleling continuous-time results, the problem is globally solvable if and only if the plant is non exponentially unstable and it is robustly globally solvable if and only if the plant is exponentially stable. We provide a constructive solution whenever the problem is solvable. Also offered is a high-performance global solution for exponentially stable plants based on receding horizon control. Illustrative simulations are included.