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

Mutti-Ur Rehman, Jehad Alzabut (), Nahid Fatima () and Sajid Khan
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Mutti-Ur Rehman: Department of Mathematics, AKFA University, Tashkent 111221, Uzbekistan
Jehad Alzabut: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
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

Mathematics, 2023, vol. 11, issue 7, 1-17

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 ) ) .

Keywords: M -matrices; Hadamard product of matrices; dynamical system; perturbed eigenvalues; singular values; structured singular values (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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