Impact of estimation errors of a matrix of transfer functions onto its analytic singular values and their potential algorithmic extraction
Bakhit, Mohammed A. and Khattak, Faizan A. and Proudler, Ian K. and Weiss, Stephan (2024) Impact of estimation errors of a matrix of transfer functions onto its analytic singular values and their potential algorithmic extraction. In: IEEE High Performance Extreme Computing Conference, 2024-09-23 - 2024-09-27. (In Press)
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Abstract
A matrix of analytic functions A(z), such as the matrix of transfer functions in a multiple-input multiple-output (MIMO) system, generally admits an analytic singular value decomposition (SVD), where the singular values themselves are functions. When evaluated on the unit circle, for the sake of analyticity, these singular values must be permitted of become negative. In this paper, we address how the estimation of such a matrix, causing a stochastic perturbation of A(z), results in fundamental changes to the analytic singular values: for the perturbed system, we show that their analytic singular values lose any algebraic multiplicities and are strictly non-negative with probability one. We present examples and highlight the impact that this has on algorithmic solutions to extracting an analytic or approximate analytic SVD.
ORCID iDs
Bakhit, Mohammed A., Khattak, Faizan A., Proudler, Ian K. and Weiss, Stephan ORCID: https://orcid.org/0000-0002-3486-7206;-
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Item type: Conference or Workshop Item(Paper) ID code: 90559 Dates: DateEvent6 September 2024Published6 September 2024AcceptedSubjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Engineering > Electronic and Electrical Engineering
Technology and Innovation Centre > Sensors and Asset ManagementDepositing user: Pure Administrator Date deposited: 13 Sep 2024 10:59 Last modified: 01 Oct 2024 15:07 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/90559