On the Applicability of the Ho-Kalman Minimal Realization Theory
The reduced-order model of a time-invariant linear dynamical system, excited by a force of an impulsive type, may be readily obtained using the Ho-Kalman minimal-realization algorithm . The method is based upon a particular factorization of the Hankel matrix in the Markovian representation of the discrete-time process. For stochastic systems, the applicability of the theory has been demonstrated by Akaike  on the assumption that the excitation is a zero-mean white noise of a gaussian type. Some of the most widely known output-only identification methods, such as Eigensystem Realization Algorithm (ERA), Canonical Variate Analysis (CVA), and Balanced Realization (BR)) are based upon the above-mentioned work, with the aid of a robust factorization technique, such as Singular-Value Decomposition (SVD). Notwithstanding the growing popularity of the above methods, some aspects of their applicability are not yet understood. Two points are of particular interest: the first regards the applicability of the theory in highly damped systems; and the second regards its applicability to systems driven by excitations different from the one hypothesized. The aim of the present work is to define a reliable test on the hypotheses. Some numerical and experimental results are presented.
L. Garibaldi, C. Surace, K. Holford and W.M. Ostachowicz
R. Spadavecchia et al., "On the Applicability of the Ho-Kalman Minimal Realization Theory", Key Engineering Materials, Vol. 347, pp. 133-138, 2007