A Mathematical Tool to Investigate the Stability Analysis of Structured Uncertain Dynamical Systems with M-Matrices
Mutti-Ur RehmanDepartment of Mathematics, AKFA University, Tashkent 111221, UzbekistanJehad AlzabutDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaNahid FatimaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaSajid Ullah KhanDepartment of Computer Science, Sukkur IBA University, Sukkur 65200, Pakistan
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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)TΔ(t)+Δ(t)(A∘B)).
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