Robustness of ISS systems to inputs with limited moving average: Application to spacecraft formations

We provide a theoretical framework that fits realistic challenges related to spacecraft formation with disturbances. We show that the input-to-state stability of such systems guarantees some robustness with respect to a class of signals with bounded average-energy, which encompasses the typical disturbances acting on spacecraft formations. Solutions are shown to converge to the desired formation, up to an offset, which is somewhat proportional to the considered moving average of disturbances. In the presence of fast peaking perturbations, the approach provides a tighter evaluation of the disturbances' influence, which allows for the use of more parsimonious control gains