Polynomial-Type Lyapunov-Krasovskii Functional and Jacobi-Bessel Inequality: Further Results on Stability Analysis of Time-Delay Systems

• 成果类型: Article
• 署名作者: Huang, Yi-Bo; He, Yong; An, Jianqi; Wu, Min
• 署名单位: China University of Geosciences
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3013930
• 发表日期: 2021
• 页码: 2905-2912
• 关键词: Stability criteria; DELAYS; Numerical stability; Symmetric matrices; Integral equations; Jacobian matrices; Integral inequality; multiple integral term; stability analysis; time-delay system

摘要

To derive a less conservative stability criterion via Lyapunov-Krasovskii functional (LKF) method, in previous literature, multiple integral terms are usually introduced into the construction of LKFs. This article generalizes the results of previous literature by proposing a polynomial-type LKF, which contains the LKFs with multiple integral terms as special cases. In addition, a Jacobi-Bessel inequality is presented to bound the derivative of such LKF. As a result, an improved stability criterion of time-delay systems is established. Finally, two numerical examples are given to illustrate the effectiveness, and advantages of our method.