Diagonal solutions for a class of linear matrix inequality

Ali Algefary; Ali Algefary

doi:10.3934/math.20241286

AIMS Mathematics

2024, Volume 9, Issue 10: 26435-26445. doi: 10.3934/math.20241286

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Diagonal solutions for a class of linear matrix inequality

Ali Algefary ^,

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

Received: 09 July 2024 Revised: 27 August 2024 Accepted: 03 September 2024 Published: 11 September 2024
MSC : 15A45, 15B48, 34D20, 37C75, 93D05

In this paper, we present a characterization of diagonal solutions for a class of linear matrix inequalities. We consider linear hybrid time-delay systems and explore the conditions under which these systems are positive and asymptotically stable. Specifically, we investigate the existence of positive diagonal solutions for a linear inequality when the system matrices are Metzler and nonnegative. Using various mathematical tools, including the Schur complement and separation theorems, we derive necessary and sufficient conditions for the stability of these systems. Our results extend existing stability criteria and provide new insights into the stability analysis of positive time-delay systems.
- diagonal stability,
- positive definite matrices,
- Lyapunov functions,
- differential equations,
- Lyapunov diagonal stability
Citation: Ali Algefary. Diagonal solutions for a class of linear matrix inequality[J]. AIMS Mathematics, 2024, 9(10): 26435-26445. doi: 10.3934/math.20241286

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Abstract

In this paper, we present a characterization of diagonal solutions for a class of linear matrix inequalities. We consider linear hybrid time-delay systems and explore the conditions under which these systems are positive and asymptotically stable. Specifically, we investigate the existence of positive diagonal solutions for a linear inequality when the system matrices are Metzler and nonnegative. Using various mathematical tools, including the Schur complement and separation theorems, we derive necessary and sufficient conditions for the stability of these systems. Our results extend existing stability criteria and provide new insights into the stability analysis of positive time-delay systems.

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