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Appendix A Bibliography
Xmath Model Reduction Module A-2 ni.com
[GrA90] M. Green and BDO Anderson, “Generalized balanced stochastic truncation,”
Proceedings for 29th CDC, 1990.
[Gre88] M. Green, “Balanced stochastic realization,” Linear Algebra and Applications, Vol. 98,
1988, pp. 211–247.
[Gre88a] M. Green, “A relative error bound for balanced stochastic truncation,” IEEE Transactions
on Automatic Control, Vol. 33, 1988, pp. 961–965.
[HiP90] D. Hinrichsen and A J Pritchard, “An improved error estimate for reduced-order models
of discrete-time systems,” IEEE Transactions on Automatic Control, Vol. 35, 1990,
pp. 317–320.
[LAL90] Y. Liu, BDO Anderson, and U-L Ly, “Coprime factorization controller reduction with
Bezout identity induced frequency weighting,” Automatica, Vol. 26, No. 2, 1990,
pp. 233–249.
[Lau80] A. J. Laub, “On computing ‘balancing’ transformations,” Proceedings on Joint American
Controls Conference, San Francisco, CA, 1980, Section FA8-E.
[LHPW87] A. J. Laub, M. T. Heath, C. C. Paige, and R. C. Ward, “Computation of system balancing
transformations and other applications of simultaneous diagonalizing algorithms,” IEEE
Transactions on Automatic Control, Vol. AC-32, 1987, pp. 115–122.
[LiA86] Y. Liu and BDO Anderson, “Controller reduction via stable factorization and balancing,”
Int. J. Control, Vol. 44, 1986, pp. 507–531.
[LiA89] Y. Liu and BDO Anderson, “Singular perturbation approximation of balanced systems,”
International Journal of Control, Vol. 50, 1989, pp. 1379–1405.
[LiA90] Y. Liu and BDO Anderson, “Frequency weighted controller reduction methods and loop
transfer recovery,” Automatica, Vol. 26, No. 3, pp. 487–489.
[Moo81] B.C. Moore, “Principal component analysis in linear systems: Controllability,
observability and model reduction,” IEEE Transactions on Automatic Control,
Vol. AC-26, No. 1, 1981, pp. 17–32.
[NJB84] C. N. Nett, C. A. Jacobson, and M. J. Balas, “A connection between state-space
and doubly coprime fractional representations,” IEEE Transactions on Automatic
Control, Vol. AC-29, 1984, pp. 831–832.
[PeS82] L. Pernebo, and L. M. Silverman, “Model reduction via balanced state space
representations,” IEEE Transactions on Automatic Control, Vol. AC-27, No. 2, 1982,
pp. 382–387.