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Stewart, Michael Alan 2011-05-07T12:32:37Z 2011-05-07T12:32:37Z 10000-01-01 1996 This thesis considers problems of stability, rank estimation and conditioning for structured matrices. The ideas are developed with attention to potential applications in control and signal processing where such matrices arise routinely. A stability result for the factorization of the broad class of positive definite Toeplitz-like matrices is given. For nearly semidefinite Toeplitz matrices, it is proven that the Cholesky factor has a limited rank-revealing property. This property has a close connection with a stability result for the Schur algorithm for the factorization of a positive definite Toeplitz matrix. An attempt is made to extend the connection between Cholesky factors and conditioning to block-Toeplitz matrices by considering fundamental properties that govern the conditioning of transformations used in fast algorithms for the factorization of such matrices. A quotient URV decomposition is introduced and applied to block Toeplitz matrices to provide an on-line algorithm for the solution of the multi-input/multi-output (MIMO) state space identification problem. Finally, theoretical results are given that relate to the problem of determining the distance of a state space model from a state space model that is non-minimal. This may be interpreted as an attempt to show that the problem of determining when a state-space model is nearly uncontrollable or unobservable is well-posed. Made available in DSpace on 2011-05-07T12:32:37Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712446.pdf: 6707963 bytes, checksum: a7b74a6d268b099b4ddb5c84fa8117a9 (MD5) Previous issue date: 1996 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:42:25Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:18:26-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only 9780591200034 AAI9712446 (UMI)AAI9712446 http://hdl.handle.net/2142/20219 eng Copyright 1996 Stewart, Michael Alan Mathematics Engineering, Electronics and Electrical Structured linear algebra problems and applications to system identification text Electrical and Computer Engineering Electrical Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.