Stability Analysis of Linear Time-Varying Delay Systems via a Novel Augmented Variable Approach

Wenqi Liao, Hongbing Zeng () and Huichao Lin
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Wenqi Liao: School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China
Hongbing Zeng: School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China
Huichao Lin: College of Information Science and Engineering, Northeastern University, Shenyang 110819, China

Mathematics, 2024, vol. 12, issue 11, 1-14

Abstract: This paper investigates the stability issues of time-varying delay systems. Firstly, a novel augmented Lyapunov functional is constructed for a class of bounded time-varying delays by introducing new double integral terms. Subsequently, a time-varying matrix-dependent zero equation is introduced to relax the constraints of traditional constant matrix-dependent zero equations. Secondly, for a class of periodic time-varying delays, considering the monotonicity of the delay and combining it with an augmented variable approach, Lyapunov functionals are constructed for monotonically increasing and monotonically decreasing delay intervals, respectively. Based on the constructed augmented Lyapunov functionals and the employed time-varying zero equation, less conservative stability criteria are obtained separately for bounded and periodic time-varying delays. Lastly, three examples are used to verify the superiority of the stability conditions obtained in this paper.

Keywords: stability analysis; augmented variable; time-delay systems; time-varying delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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