We propose a cord distance in the space of dynamical models that takes into account their dynamics, including transients, output maps and input distributions. In data analysis applications, as opposed to control, the input is often not known and is inferred as part of the (blind) identification. So it is an integral part of the model that should be considered when comparing different time series. Previous work on kernel distances between dynamical models assumed either identical or independent inputs. We extend it to arbitrary distributions, highlighting connections with system identification, independent component analysis, and optimal transport. The increased modeling power is demonstrated empirically on gait classification from simple visual features.