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

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

2024 | Wei Wang, Jinming Liang, Mihan Liu, Liming Ding, Hongbing Zeng
This paper addresses the issue of absolute stability for uncertain Lur'e systems with time-varying delay using a delay-segmentation approach. The method involves decomposing the delay interval into two subintervals of unequal lengths, allowing 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 results are less conservative and provide a more accurate assessment of absolute stability. The effectiveness of the proposed approach is demonstrated through a numerical example. The paper also introduces two stability criteria and provides detailed definitions and lemmas to support the main results.This paper addresses the issue of absolute stability for uncertain Lur'e systems with time-varying delay using a delay-segmentation approach. The method involves decomposing the delay interval into two subintervals of unequal lengths, allowing 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 results are less conservative and provide a more accurate assessment of absolute stability. The effectiveness of the proposed approach is demonstrated through a numerical example. The paper also introduces two stability criteria and provides detailed definitions and lemmas to support the main results.
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