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On worst-case approximation of feasible system sets via orthonormal basis functions

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3 Author(s)
Casini, M. ; Dipt. di Ingegneria dell''Informazione, Siena Univ., Italy ; Garulli, A. ; Vicino, A.

This paper deals with the approximation of sets of linear time-invariant systems via orthonormal basis functions. This problem is relevant to conditional set membership identification, where a set of feasible systems is available from observed data, and a reduced-complexity model must be estimated, within a linearly parameterized model class. The basis of the model class is a collection of impulse responses of linear filters (e.g. Laguerre functions), whose poles must be chosen properly. The objective of the paper is to select the basis function pole according to a worst-case optimality criterion taking into account the uncertainty system set. This leads to complicated min-max optimization problems. Suboptimal conditional identification algorithms are introduced and tight bounds are provided on the associated identification errors

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Decision and Control, 2001. Proceedings of the 40th IEEE Conference on  (Volume:3 )

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