Interconnection Between Schur Stability and Structured Singular Values Article Swipe

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Mujeeb ur Rehman , Jehad Alzabut , Muhammad Tayyab , Fouzia Amir ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.37256/cm.6120255707

In this paper, we present new results on the interconnections between Schur stability and structured singular values of real-valued matrices, denoted as Rn×n . Most new findings are obtained for n = 2 and n = 3. These novel insights into the relationship between Schur stability and structured singular values are developed by applying various tools from linear algebra, system theory, and matrix analysis. Schur stability ensures that all eigenvalues lie within the unit circle in the complex plane, which is fundamental for the boundedness and stability of system responses. Structured singular values, on the other hand, provide a measure of robustness, stability, and performance against structured perturbations in system parameters, offering valuable insights into the stability margins and performance limits under such uncertainties.

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Mathematical Analysis

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Mathematics Singular value Eigenvalues and eigenvectors Interconnection Complex plane Unit circle Stability (learning theory) Pure mathematics Robustness (evolution) Schur complement Schur decomposition Algebra over a field Mathematical analysis Computer science Gene Biochemistry Physics Machine learning Computer network Chemistry Quantum mechanics

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Type: article
Language: en
Landing Page: https://doi.org/10.37256/cm.6120255707
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Title: Interconnection Between Schur Stability and Structured Singular Values

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Publication year: 2024

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Authors: Mujeeb ur Rehman, Jehad Alzabut, Muhammad Tayyab, Fouzia Amir

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Concepts: Mathematics, Singular value, Eigenvalues and eigenvectors, Interconnection, Complex plane, Unit circle, Stability (learning theory), Pure mathematics, Robustness (evolution), Schur complement, Schur decomposition, Algebra over a field, Mathematical analysis, Computer science, Gene, Biochemistry, Physics, Machine learning, Computer network, Chemistry, Quantum mechanics

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abstract_inverted_index.boundedness	84
abstract_inverted_index.eigenvalues	69
abstract_inverted_index.fundamental	81
abstract_inverted_index.parameters,	110
abstract_inverted_index.performance	104, 119
abstract_inverted_index.real-valued	18
abstract_inverted_index.robustness,	101
abstract_inverted_index.relationship	42
abstract_inverted_index.perturbations	107
abstract_inverted_index.uncertainties.	123
abstract_inverted_index.interconnections	9
cited_by_percentile_year
countries_distinct_count	2
institutions_distinct_count	4
citation_normalized_percentile.value	0.35886932
citation_normalized_percentile.is_in_top_1_percent	False
citation_normalized_percentile.is_in_top_10_percent	False