Balancing three matrices in control theory

Nela Bosner


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.


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

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ISSN: 1331-0623 (Print), 1848-8013 (Online)