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Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. (English) Zbl 0624.93025
The system balancing introduced by B. C. Moore [SIAM J. Sci. Stat. Comput. 7, 1147-1159 (1986; Zbl 0607.65013)] as a tool for system reduction is treated from the numerical point of view. The authors apply their algorithm [ibid. AC-26, 17-32 (1981; Zbl 0464.93022)] to the computation of the singular value decomposition of a product of matrices. They compute the contragredient transformation which diagonalizes both observability and reachability Gramians. They compute Cholesky factors of the Gramians, compute singular value decompositions of the product of the Cholesky factors, form contragredient transformations and form the balanced state-space matrices.
Reviewer: A.Vaněček

MSC:
93B40 Computational methods in systems theory (MSC2010)
65F99 Numerical linear algebra
93C05 Linear systems in control theory
15A18 Eigenvalues, singular values, and eigenvectors
93B05 Controllability
93B07 Observability
93B17 Transformations
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