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A Jacobi-type method for computing balanced realizations

✍ Scribed by U. Helmke; K. Hüper

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
162 KB
Volume
39
Category
Article
ISSN
0167-6911

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✦ Synopsis

A new numerical scheme for computing balancing coordinate transformations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and nonorthogonal Jacobi-type rotations is considered. The algorithm is shown to be globally convergent to a balancing transformation that arranges the Hankel singular values in a prescribed ordering. Local quadratic convergence of the algorithm is shown.

📜 SIMILAR VOLUMES

Balancing related methods for minimal re
Balancing related methods for minimal realization of periodic systems
✍ A Varga 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 112 KB

We propose balancing related numerically reliable methods to compute minimal realizations of linear periodic systems with time-varying dimensions. The ÿrst method belongs to the family of square-root methods with guaranteed enhanced computational accuracy and can be used to compute balanced minimal