Stability Preservation of Stochastic Systems With Over Large Variable Time Delays

• 成果类型: Article
• 署名作者: Zhao, Xueyan; Deng, Feiqi
• 署名单位: South China University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3095460
• 发表日期: 2022
• 页码: 3273-3288
• 关键词: Lyapunov function; stabilization; stochastic systems (SSs); variable time delays; pth moment stability

摘要

This article aims to reveal an interesting phenomenon about the time delays (TDs) in control systems: stability preservation with over large intermittently or unbounded variable TDs. That is, given a system asymptotically stable for bounded TDs, it could remain to be stable when the TDs are enhanced to have peak values over large intermittently or unbounded. The investigation is carried out by theoretical analysis plus case studies with the stochastic system models. The stability of systems is the core issue; the explicit involvement of the TDs in the stability criteria is the premise for them being concerned. To these ends, a series of lemmas are established preliminarily, a new type stability theorem with its practical version is established in succession, and a stability criterion with the TDs as explicit parameters is induced. The Lyapunov function method is applied for less restriction and conservativeness. The mechanism and the approach for the emergence of the phenomenon under probe are analyzed. Implementation is considered for the linear system model. Typical variable TDs are constructed for illustrations theoretically. Finally, the obtained results are verified with numerical experiments.