Stability analysis of linear systems with a periodical time-varying delay based on an improved non-continuous piecewise Lyapunov functional

Wei Wang; Chang-Xin Li; Ao-Qian Luo; Hui-Qin Xiao; Wei Wang; Chang-Xin Li; Ao-Qian Luo; Hui-Qin Xiao

doi:10.3934/math.2025418

AIMS Mathematics

2025, Volume 10, Issue 4: 9073-9093. doi: 10.3934/math.2025418

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Research article

Stability analysis of linear systems with a periodical time-varying delay based on an improved non-continuous piecewise Lyapunov functional

1.
Department of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, 412007, Hunan, China
2.
Department of Transportation, Hunan University of Technology, Zhuzhou, 412007, Hunan, China

Received: 30 December 2024 Revised: 28 March 2025 Accepted: 09 April 2025 Published: 21 April 2025
MSC : 34D20, 34K20, 34K25

This paper mainly studies the stability of linear systems with a periodical time-varying delay. An improved delay-segmentation-based non-continuous piecewise Lyapunov–Krasovskii (L–K) functional is proposed. In comparison with the currently available L–K functional, this functional incorporates more delay-segmentation-interval-related information. Additionally, it effectively eases the boundary constraints at each segment point. Consequently, a stability criterion with reduced conservativeness for linear time-delay systems is derived. Finally, two numerical examples and a single-area load frequency control system are given to validate the efficiency of the proposed approach.
- periodical time-varying delay,
- delay segmentation,
- Lyapunov–Krasovskii functional,
- stability criteria
Citation: Wei Wang, Chang-Xin Li, Ao-Qian Luo, Hui-Qin Xiao. Stability analysis of linear systems with a periodical time-varying delay based on an improved non-continuous piecewise Lyapunov functional[J]. AIMS Mathematics, 2025, 10(4): 9073-9093. doi: 10.3934/math.2025418

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Abstract

This paper mainly studies the stability of linear systems with a periodical time-varying delay. An improved delay-segmentation-based non-continuous piecewise Lyapunov–Krasovskii (L–K) functional is proposed. In comparison with the currently available L–K functional, this functional incorporates more delay-segmentation-interval-related information. Additionally, it effectively eases the boundary constraints at each segment point. Consequently, a stability criterion with reduced conservativeness for linear time-delay systems is derived. Finally, two numerical examples and a single-area load frequency control system are given to validate the efficiency of the proposed approach.

References

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