Strong iISS for neutrally stable systems by saturated linear state feedback

In this note, we propose a linear state-feedback that ensures Strong iISS to any neutrally stable system affected by actuator saturation. This robustness property was recently proposed as a compromise between the strength of input-to-state stability (ISS) and the generality of integral input-to-state stability (iISS). It ensures not only that the system is globally asymptotically stable in the absence of disturbances, but also that trajectories are bounded in response to any perturbation whose amplitude is below a certain threshold. It also guarantees that the state converges to the origin in response to any vanishing disturbance. Here Strong iISS is proven with respect to any additive disturbance acting outside the saturation, without any matching requirement.