New results on delay-dependent stability conditions for uncertain linear systems with two additive time-varying delays

Volume 39, Issue 3, pp 398--406 https://dx.doi.org/10.22436/jmcs.039.03.08

Publication Date: April 15, 2025 Submission Date: October 04, 2024 Revision Date: January 06, 2025 Accteptance Date: February 28, 2025

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Authors

J. Piyawatthanachot - Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand. K. Mukdasai - Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand.

Abstract

In this study, we explore a novel delay-dependent criterion for asymptotic stability in linear systems with two additive time-varying delays and nonlinear perturbations. By utilizing the Newton-Leibniz formula, the extended Jensen's double integral inequality, the extended Wirtinger's integral inequality, a novel Lyapunov-Krasovskii functional and the application of zero equations, we derive sufficient conditions for the system's asymptotic stability in the form of linear matrix inequalities. Additionally, we introduce new delay-dependent stability conditions specifically for these linear systems with two additive time-varying delays. Numerical examples are provided to illustrate the feasibility and effectiveness of the theorems.

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Keywords

• Delay-dependent asymptotic stability
• two additive time-varying delays
• extended Jensen's double integral inequality
• linear matrix inequality

MSC

•  34K25
•  93C10
•  93D09
•  34D20

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