Abstract
This paper studies the stability analysis problem for time-varying delay systems. An appropriate Lyapunov-Krasovskii functional (LKF) is constructed where its derivative is a quadratic polynomial function of the delay. A novel negative condition of the mentioned quadratic function with two variable parameters is developed to ensure that the LKF derivative is negative, reducing conservatism on some similar results. Besides, an extended version of Bessel-Legendre inequality is introduced to be employed in the stability analysis of time-varying delay systems. Then, some stability criteria with less conservatism are derived for two kinds of the time-varying delay. Finally, the effectiveness of the proposed stability criteria is demonstrated through three examples.
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This work is supported in part by the National Natural Science Foundation of China (Grant Nos. 61890924, 61991404).
Yun Chen received his B.Sc. degree in electrical engineering and automation from the Shaoyang University, Shaoyang, China, in 2017, and an M.Sc. degree in control theory and control engineering from the Hunan University of Technology, Zhuzhou, China, in 2020. He is currently an assistant at Hunan City University, Yiyang, China. His current research interests include time-delay systems, neural networks, and networked state estimation.
Yaqi Li received her B.Sc. and M.Sc. degrees from Hunan University of Technology, in 2016 and 2020, respectively. She is a research worker in National Innovation Center of Advanced Rail Transit Equipment, Zhuzhou, China. Her research interests include time-delay systems, robust control, and machine learning.
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Chen, Y., Li, Y. Stability Analysis for Time-delay Systems via a Novel Negative Condition of the Quadratic Polynomial function. Int. J. Control Autom. Syst. 19, 3159–3167 (2021). https://doi.org/10.1007/s12555-020-0468-8
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DOI: https://doi.org/10.1007/s12555-020-0468-8