an:04014543
Zbl 0624.93025
Laub, Alan J.; Heath, Michael T.; Paige, Chris C.; Ward, Robert C.
Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
EN
IEEE Trans. Autom. Control 32, 115-122 (1987).
00152492
1987
j
93B40 65F99 93C05 15A18 93B05 93B07 93B17
system balancing; system reduction; contragredient transformation; observability and reachability Gramians; Cholesky factors; singular value decompositions
The system balancing introduced by \textit{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.
A.Van????ek
Zbl 0607.65013; Zbl 0464.93022