System identifiability from finite time series

The possibility to identify linear systems from finite data, e.g. a partial impulse response, is determined by the degree of corroboration of system restrictions by the observed data. Ala~'Kt-In this paper we investigate the identification of systems from time series observed over a finite time interval. The data generating system is supposed to be finite dimensional, linear and time invariant, but not necessarily controllable. The minimal number of time series needed to identify a system is characterized by the identifiability index of a system, which measures the rank drop of autoregressive representations. We formulate a procedure for modelling finite time series which takes the corroboration of system restrictions into account. This also gives a new solution for the partial realization problem.