Linear system approximation via covariance equivalent realizations

Robust controller design based on reduced order plants

“…Computationally attractive methods such as Pade´, modal, or continued-fraction approximations or moment matching methods generally have no guaranteed stability/performance. The balanced realization method (Moore 1981), the Hankel norm approximation method (Adamjan et al 1971, Kung and Lin 1981, Glover 1984, and the q-covariance equivalent method (Yousuff et al 1985) are among rigorous model reduction methods that come with some kind of a performance criterion. The closed-loop performance of such order reduction methods when used for the purpose of control system design was studied recently.…”

An iterative SVD-Krylov based method for model reduction of large-scale dynamical systems

“…Several numerical examples from various disciplines verify the effectiveness of the proposed approach. It performs significantly better than the q-cover [60,59] and the least-squares [33] methods that have a similar projection structure to the proposed method. Also, in terms of both the H2 and H∞ error measures, its performance is comparable to or sometimes better than that of balanced truncation.…”

“…al. in [18,60,59]. Grimme [26] showed how one can obtain the required projection in a numerically efficient way using the rational Krylov method of Ruhe [53], hence showed how to solve the moment matching (multi-point rational interpolation) problem using the Krylov projection methods in an effective way.…”

“…in [18,60,59]. In [60] and [59], the dual projection is used where Q is replaced by P and V is chosen as the observability matrix of order r leading to the so-called q-cover realizations.…”

“…In [60] and [59], the dual projection is used where Q is replaced by P and V is chosen as the observability matrix of order r leading to the so-called q-cover realizations. Moreover, in [18], these results were generalized to the case where V was replaced by a rational Krylov subspace.…”