On the structure of balanced and other principal representations of SISO systems

“…The difficulty (pointed out earlier) of working with two Lyapunov equations separately, as proposed in [48], has led to the consideration of a different approach which is based upon the notion of a cross grammian that was introduced in [28]. The cross grammian .…”

Section: Svd-krylov-based Approximation Methodsmentioning

confidence: 99%

Approximation of Large-Scale Dynamical Systems: An Overview

Antoulas

2004

IFAC Proceedings Volumes

146

179

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In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish among three basic categories, namely the SVD-based, the Krylov-based and the SVD-Krylov-based approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two.

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“…Since any balanced realization of a SISO-system can be shown to be signsymmetric with respect to the entries in A, B and C (cf. [14] and [6]), we can describe a procedure to compute a positive reduced order model of a SISO-system, by just comparing signs in the sign-symmetric realization. In the worst case, this procedure only allows for the scalar approximation mentioned above, but in practical examples, it yields positive approximations also of higher order with an acceptable error bound.…”

Section: {ẋ (T) = Ax(t) + Bu(t) Y(t) = Cx(t) + Du(t)mentioning

confidence: 99%