Partial Singular Value Assignment for Large-Scale Systems

Huang, Yiting; Tang, Qiong; Yu, Bo

doi:10.3390/axioms12111012

Open AccessArticle

Partial Singular Value Assignment for Large-Scale Systems

by

Yiting Huang

,

Qiong Tang

and

Bo Yu

^*

School of Science, Hunan University of Technology, Zhuzhou 412007, China

^*

Author to whom correspondence should be addressed.

Axioms 2023, 12(11), 1012; https://doi.org/10.3390/axioms12111012

Submission received: 15 September 2023 / Revised: 18 October 2023 / Accepted: 24 October 2023 / Published: 27 October 2023

(This article belongs to the Special Issue Control Theory and Control Systems: Algorithms and Methods)

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Abstract

The partial singular value assignment problem stems from the development of observers for discrete-time descriptor systems and the resolution of ordinary differential equations. Conventional techniques mostly utilize singular value decomposition, which is unfeasible for large-scale systems owing to their relatively high complexity. By calculating the sparse basis of the null space associated with some orthogonal projections, the existence of the matrix in partial singular value assignment is proven and an algorithm is subsequently proposed for implementation, effectively avoiding the full singular value decomposition of the existing methods. Numerical examples exhibit the efficiency of the presented method.

Keywords: partial singular value assignment; large-scale system; sparse basis; orthogonal projection

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MDPI and ACS Style

Huang, Y.; Tang, Q.; Yu, B. Partial Singular Value Assignment for Large-Scale Systems. Axioms 2023, 12, 1012. https://doi.org/10.3390/axioms12111012

AMA Style

Huang Y, Tang Q, Yu B. Partial Singular Value Assignment for Large-Scale Systems. Axioms. 2023; 12(11):1012. https://doi.org/10.3390/axioms12111012

Chicago/Turabian Style

Huang, Yiting, Qiong Tang, and Bo Yu. 2023. "Partial Singular Value Assignment for Large-Scale Systems" Axioms 12, no. 11: 1012. https://doi.org/10.3390/axioms12111012

APA Style

Huang, Y., Tang, Q., & Yu, B. (2023). Partial Singular Value Assignment for Large-Scale Systems. Axioms, 12(11), 1012. https://doi.org/10.3390/axioms12111012

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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