Input-to-State Stability of Impulsive Delay Systems With Multiple Impulses

• 成果类型: Article
• 署名作者: Li, Peng; Li, Xiaodi; Lu, Jianquan
• 署名单位: Shandong Normal University; Southeast University - China
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2982156
• 发表日期: 2021
• 页码: 362-368
• 关键词: Delay systems; Delay effects; Numerical stability; Stability criteria; Symmetric matrices; Nonlinear systems; impulsive systems; input-to-state stability (ISS); Lyapunov method; multiple impulses; time delay

摘要

This article investigates input-to-state stability (ISS) of impulsive delay systems with multiple impulses. We provide sufficient conditions in terms of exponential ISS-Lyapunov functions coupled with Razumikhin-type conditions for establishing the ISS property, where the possibility of the effects of multiple impulses on ISS is fully considered. It shows that when the continuous dynamics are ISS and the discrete dynamics that govern the jumps involve multiple impulses, the ISS property can be retained for arbitrary impulse time sequences if the cumulative strength of multiple impulses satisfies some conditions. Conversely, when the continuous dynamics are not ISS, then the multiple impulses that satisfy some conditions can stabilize the system in ISS sense if there are no overly long intervals between impulses. Two illustrative examples are presented, with their numerical simulations, to demonstrate the main results.