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Smoothly time varying systems and Toeplitz least squares problems

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2 Author(s)
M. Stewart ; Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA ; P. Van Dooren

This paper explores the implications of assuming a system to be smoothly time-varying for least squares based system identification, as well as conditions under which least squares solutions are smoothly time-varying. By requiring persistent excitation and that the order of the model be chosen appropriately, using a standard singular value based scheme, it is shown that the subspace tracking, least squares and total least squares problems all yield smooth solutions. Specific tracking bounds are given, which-show that any smooth system which realizes the input/output relation with small error must be close to the least squares solution. This indicates that if smoothness is desired, the least squares estimate is a reasonable choice. The underlying matrix problem has Toeplitz structure which can be exploited in the algorithmic implementation.

Published in:

American Control Conference, 1994  (Volume:3 )

Date of Conference:

29 June-1 July 1994