Balancing three matrices in control theory

Nela Bosner

Vol. 19 No. 3 (2014)
Special Issue: Proceedings of the 8th Conference on Applied Mathematics and Scientific Computing, Šibenik, Croatia, 2013

8th Conference on Applied Mathematics and Scientific Computing

Balancing three matrices in control theory

Published 2014-10-17

Nela Bosner

Nela Bosner
Department of Mathematics, University of Zagreb

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Abstract

Several problems from control theory are presented which are sensitive to badly scaled matrices. We were specially concerned with the algorithms involving three matrices, thus we extended the Ward's balancing algorithm for two matrices. Numerical experiments confirmed that balancing three matrices can produce an accurate frequency response matrix for descriptor linear systems, it can also improve the solution of the pole assignment problem via state feedback and the determination of the controllable part of the system.

Keywords

balancing three matrices, diagonal transformations, numerical stability, frequency response matrix, pole assignment problem, controllable part of the system

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Supplementary File(s)

LaTeX source Magnitude of the computed frequency response matrices, example 1 Magnitude of the computed frequency response matrices, example 2 Magnitude of the computed frequency response matrices, example 3 Maximal magnitude of elements for the original matrix and the balanced matrix B Magnitude ranges of elements for the original matrix and the balanced matrix B. Desired poles and the computed poles. Desired poles and the computed poles, inner region.