The l2l2 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 l2l2 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 [A.R. Teel, N. Kapoor, The L2L2 anti-windup problem: its definition and solution, in: Proceedings of the 4th ECC, Brussels, Belgium, July 1997], 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.