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Measurement noise error bounds for eigensystem realization algorithm

This paper studies the identification of linear discrete-time time-invariant finite-dimensional systems using Markov parameters. It is shown that the eigensystem realisation algorithm (ERA) and Ho-Kalman realizations are special cases of a more general construction for obtaining minimal realizations from decompositions of the Markov block Hankel matrix. An upper bound for the error between the system and the reduced-order model formed from truncation of the ERA realization of the noisy Markov block Handel matrix is given. Finally, numerical computation of this new upper bound are given to illustrate these results.