Stability analysis of systems with additive time-varying delays via new bivariate quadratic reciprocally convex inequality

Xiao Ge; Xinzuo Ma; Yuanyuan Zhang; Han Xue; Seakweng Vong; Xiao Ge; Xinzuo Ma; Yuanyuan Zhang; Han Xue; Seakweng Vong

doi:10.3934/math.20241721

AIMS Mathematics

2024, Volume 9, Issue 12: 36273-36292. doi: 10.3934/math.20241721

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Research article

Stability analysis of systems with additive time-varying delays via new bivariate quadratic reciprocally convex inequality

1.
College of Science, Nanjing Forestry University, Nanjing 210037, China
2.
Department of Mathematics, University of Macau, Avenida da Universidade, Macau, China

Received: 20 November 2024 Revised: 18 December 2024 Accepted: 24 December 2024 Published: 30 December 2024
MSC : 34K20, 93C05

This paper focuses on the stability analysis of additive time-varying delay systems. First, a bivariate quadratic reciprocally convex matrix inequality is derived, which serves as a generalization of traditional reciprocally convex inequalities. By applying the Lyapunov–Krasovskii functional method, this matrix inequality is incorporated to form a new stability criterion applicable to systems with additive time-varying delays. Finally, some numerical examples are presented to demonstrate the effectiveness of the theoretical results obtained.
- stability,
- reciprocally convex inequality,
- Lyapunov–Krasovskii functional method,
- additive time-varying delay
Citation: Xiao Ge, Xinzuo Ma, Yuanyuan Zhang, Han Xue, Seakweng Vong. Stability analysis of systems with additive time-varying delays via new bivariate quadratic reciprocally convex inequality[J]. AIMS Mathematics, 2024, 9(12): 36273-36292. doi: 10.3934/math.20241721

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Abstract

This paper focuses on the stability analysis of additive time-varying delay systems. First, a bivariate quadratic reciprocally convex matrix inequality is derived, which serves as a generalization of traditional reciprocally convex inequalities. By applying the Lyapunov–Krasovskii functional method, this matrix inequality is incorporated to form a new stability criterion applicable to systems with additive time-varying delays. Finally, some numerical examples are presented to demonstrate the effectiveness of the theoretical results obtained.

References

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