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

Ali Algefary; Ali Algefary

doi:10.3934/math.20241001

AIMS Mathematics

2024, Volume 9, Issue 8: 20612-20626. doi: 10.3934/math.20241001

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

Ali Algefary ^,

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

Received: 19 May 2024 Revised: 09 June 2024 Accepted: 13 June 2024 Published: 25 June 2024
MSC : 15A45, 15B48, 34D20, 37C75, 93D05

Using the Khatri-Rao product, we presented new characterizations for the common Lyapunov diagonal stability for a family of real matrices $ \mathcal{A} $. For special partitions $ \alpha $, we used the notion of $ \mathcal{P}^{\alpha} $-sets and common $ \alpha $-scalar Lyapunov stability to formulate further characterizations. Furthermore, generalizations of these results to the common $ \alpha $-scalar Lyapunov stability were developed. Our goal of this paper was to unify and enhance relevant work.
- Lyapunov functions,
- matrix stability,
- matrix Lyapunov inequality,
- diagonal solution,
- large scale systems,
- positive definite matrix,
- Khatri-Rao product
Citation: Ali Algefary. A characterization of common Lyapunov diagonal stability using Khatri-Rao products[J]. AIMS Mathematics, 2024, 9(8): 20612-20626. doi: 10.3934/math.20241001

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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 $ \mathcal{A} $. For special partitions $ \alpha $, we used the notion of $ \mathcal{P}^{\alpha} $-sets and common $ \alpha $-scalar Lyapunov stability to formulate further characterizations. Furthermore, generalizations of these results to the common $ \alpha $-scalar Lyapunov stability were developed. Our goal of this paper was to unify and enhance relevant work.

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