The Dual Characterization of Structured and Skewed Structured Singular Values

Mutti-Ur Rehman, Jehad Alzabut, Taqwa Ateeq, Jutarat Kongson and Weerawat Sudsutad
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Mutti-Ur Rehman: Department of Mathematics, Akfa University, Tashkent 111221, Uzbekistan
Jehad Alzabut: Deparment of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Taqwa Ateeq: Department of Applied Mathematics, Arab American University, Jenin 44862, Palestine
Jutarat Kongson: Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
Weerawat Sudsutad: Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand

Mathematics, 2022, vol. 10, issue 12, 1-10

Abstract: The structured singular values and skewed structured singular values are the well-known mathematical quantities and bridge the gap between linear algebra and system theory. It is well-known fact that an exact computation of these quantities is NP-hard. The NP-hard nature of structured singular values and skewed structured singular values allow us to provide an estimations of lower and upper bounds which guarantee the stability and instability of feedback systems in control. In this paper, we present new results on the dual characterization of structured singular values and skewed structured singular values. The results on the estimation of upper bounds for these two quantities are also computed.

Keywords: eigenvalues; singular values; structured singular values; skewed structured singular values (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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