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We show how optimal Hankel-norm approximations of dy- namical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting 'balanced trajectories', i.e., by disconnecting the past and future in the input-output pairs relating to left- and right singular vectors of the system. A self-contained proof of opti- mality is given, and formulas are derived in terms of Faddeev sequences. Some parallels with the literature are briefly indi- cated.

Optimal Hankel Norm Model Reduction By Truncation Of Trajectories