A Lyapunov--Krasovskii Method for Semiglobal Stabilization of a Class of Time-Delay Nonlinear Systems With Uncontrollable Linearization by Linear Feedback

• 成果类型: Article
• 署名作者: Yu, Xin; Lin, Wei
• 署名单位: Jiangsu Normal University; University System of Ohio; Case Western Reserve University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3347340
• 发表日期: 2024
• 页码: 4110-4117
• 关键词: Nonlinear systems; DELAYS; State feedback; Adaptive control; Closed loop systems; Backstepping; Aerospace electronics; Lyapunov-Krasovskii functional method; nonlinear systems with uncontrollable linearization; semiglobal asymptotic stabilization (SGAS) by linear feedback; sublevel sets in banach space; time-delay

摘要

This article presents a seemingly surprising yet simple solution to the open problem of when and how time-delay nonlinear systems with uncontrollable linearization is stabilizable by linear feedback. We show that if a less aggressive control objective, namely, semiglobal asymptotic stabilization (SGAS) instead of GAS is sought, instantaneous linear state feedback would be sufficient for the control of a class of nonlinear systems with state delays, despite the lack of local exponential stabilizability. The SGAS result is obtained by developing a novel Lyapunov--Krasovskii functional framework for the recursive construction of a set of Lyapunov--Krasovskii functionals, associated sublevel sets in Banach space, and linear state controllers systematically, which can be viewed as a semiglobal backstepping method linking Lyapunov functionals to sublevel sets in Banach space.