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A Mathematical Tool to Investigate the Stability Analysis of Structured Uncertain Dynamical Systems with M -Matrices

Author

Listed:
  • Mutti-Ur Rehman

    (Department of Mathematics, AKFA University, Tashkent 111221, Uzbekistan
    Department of Mathematics, Sukkur IBA University, Sukkur 65200, Pakistan)

  • Jehad Alzabut

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey)

  • Nahid Fatima

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Sajid Khan

    (Department of Computer Science, Sukkur IBA University, Sukkur 65200, Pakistan
    Department of Computer Science, AKFA University, Tashkent 111221, Uzbekistan)

Abstract

The μ -value or structured singular value is a prominent mathematical tool to analyze and synthesize both the robustness and performance of time-invariant systems. We establish and analyze new results concerning structured singular values for the Hadamard product of real square M -matrices. The new results are obtained for structured singular values while considering a set of block diagonal uncertainties. The targeted uncertainties are of two types, that is, pure real scalar block uncertainties and real full-block uncertainties. The eigenvalue perturbation result is utilized in order to determine the behavior of the spectrum of perturbed matrices ( A ∘ B ) Δ ( t ) and ( ( A ∘ B ) T Δ ( t ) + Δ ( t ) ( A ∘ B ) ) .

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1622-:d:1108813
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    References listed on IDEAS

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    1. 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.
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