Lyapunov Characterization of Input-to-State Stability for a Class of Impulsive Systems

• 成果类型: Article
• 署名作者: Bachmann, Patrick; Ahmed, Saeed; Bajcinca, Naim
• 署名单位: University of Wurzburg; University of Groningen; University of Groningen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3392636
• 发表日期: 2024
• 页码: 6996-7003
• 关键词: Lyapunov methods; Stability criteria; Sufficient conditions; trajectory; Time-varying systems; Perturbation methods; vectors; Input-to-state stability (ISS)-Lyapunov function; impulsive systems; infinite-dimensional systems; input-to-state stability (ISS)

摘要

We prove that the existence of an input-to-state stability (ISS)-Lyapunov function is a necessary and sufficient condition for the input-to-state stability of a class of impulsive systems over Banach spaces. A key feature of our work is that it employs time-varying ISS-Lyapunov functions as opposed to candidate ISS-Lyapunov functions, which also makes it possible to conclude ISS of impulsive systems with unstable continuous and discrete dynamics.