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Research Article | Open Access

A characterization of common Lyapunov diagonal stability using Khatri-Rao products

Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
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Abstract

Using the Khatri-Rao product, we presented new characterizations for the common Lyapunov diagonal stability for a family of real matrices A. For special partitions α, we used the notion of Pα-sets and common α-scalar Lyapunov stability to formulate further characterizations. Furthermore, generalizations of these results to the common α-scalar Lyapunov stability were developed. Our goal of this paper was to unify and enhance relevant work.

Keywords

Lyapunov functionsmatrix stabilitymatrix Lyapunov inequalitydiagonal solutionlarge scale systemspositive definite matrixKhatri-Rao product
CLC number: 15A45, 15B48, 34D20, 37C75, 93D05

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 20612-20626
DOI: 10.3934/math.20241001

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Cite this article:
Algefary A. A characterization of common Lyapunov diagonal stability using Khatri-Rao products. AIMS Mathematics, 2024, 9(8): 20612-20626. https://doi.org/10.3934/math.20241001

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Received: 19 May 2024
Revised: 09 June 2024
Accepted: 13 June 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)