Forwarding for discrete-time linear systems: Optimality and global stabilization under input saturation

We revisit the forwarding approach for the feedback stabilization of discrete-time systems in feedforward form. We show that the resulting feedback design is parametrized by a change of coordinate which is defined via a Sylvester equation. Moreover, we investigate the optimality of such a feedback by explicitly computing a quadratic cost which is minimized by the closed loop trajectories. Finally, we apply the forwarding approach to solve the problem of global stabilization of feedforward form systems which are simply stable in the presence of input saturations and time-delays.