Article

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 Industrial Engineering, OSTİM Technical University, Ankara 06374, TurkeyNahid FatimaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaSajid Ullah KhanDepartment of Computer Science, AKFA University, Tashkent 111221, Uzbekistan

Mathematicsjournal2023en

ABI

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)TΔ(t)+Δ(t)(A∘B)).

Topics

Stability and Control of Uncertain Systems Matrix Theory and Algorithms Numerical methods for differential equations

Identifiers

DOI: 10.3390/math11071622

Citations and references

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