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The Dual Characterization of Structured and Skewed Structured Singular Values

Author

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  • Mutti-Ur Rehman

    (Department of Mathematics, Akfa University, Tashkent 111221, Uzbekistan
    Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan
    These authors contributed equally to this work.)

  • Jehad Alzabut

    (Deparment of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Turkey
    These authors contributed equally to this work.)

  • 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)

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.

Suggested Citation

  • Mutti-Ur Rehman & Jehad Alzabut & Taqwa Ateeq & Jutarat Kongson & Weerawat Sudsutad, 2022. "The Dual Characterization of Structured and Skewed Structured Singular Values," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2050-:d:837736
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    References listed on IDEAS

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    1. Luo, Jinnan & Tian, Wenhong & Zhong, Shouming & Shi, Kaibo & Chen, Hao & Gu, Xian-Ming & Wang, Wenqin, 2017. "Non-fragile asynchronous H∞ control for uncertain stochastic memory systems with Bernoulli distribution," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 109-128.
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    Cited by:

    1. Mutti-Ur Rehman & Jehad Alzabut & Nahid Fatima & Sajid Khan, 2023. "A Mathematical Tool to Investigate the Stability Analysis of Structured Uncertain Dynamical Systems with M -Matrices," Mathematics, MDPI, vol. 11(7), pages 1-17, March.

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