Novel Robust Stability Criteria for Lur’e Systems with Time-Varying Delay

Wei Wang (), Jinming Liang, Mihan Liu, Liming Ding () and Hongbing Zeng
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Wei Wang: School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China
Jinming Liang: School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China
Mihan Liu: School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China
Liming Ding: School of Computer and Artificial Intelligence (School of Software), Huaihua University, Huaihua 418008, China
Hongbing Zeng: School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China

Mathematics, 2024, vol. 12, issue 4, 1-12

Abstract: This paper focuses on addressing the issue of absolute stability for uncertain Lur’e systems with time-varying delay using a delay-segmentation approach. The approach involves decomposing the delay interval into two distinct subintervals of unequal lengths. This allows for the introduction of a delay-segmentation-based augmented Lyapunov–Krasovskii functional that ensures piecewise continuity at the partition points. By selecting two sets of Lyapunov matrices for the time-varying delay in each interval, the obtained results are less conservative, providing a more accurate assessment of absolute stability. Finally, a numerical example is given to demonstrate the superiority of the delay-segmentation approach.

Keywords: Lur’e system; absolute stability; Lyapunov–Krasovskii functional; time-varying delay; delay-segmentation approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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