Invariant Manifold-Guided Impulsive Stabilization of Delay Equations

• 成果类型: Article
• 署名作者: Church, Kevin E. M.; Liu, Xinzhi
• 署名单位: McGill University; University of Waterloo
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3057988
• 发表日期: 2021
• 页码: 5997-6002
• 关键词: Delays; MANIFOLDS; Differential equations; stability analysis; Lyapunov methods; Linear matrix inequalities; Delay effects; delay systems; impulsive systems; stabilization

摘要

We propose an impulsive stabilization method for delay equations based on a reduction to the center-unstable manifold. Our approach does not make use of the constructions of Lyapunov's direct method, such as Lyapunov functions or functionals. Necessary and sufficient conditions for when a system can be stabilized by impulses are derived based on these ideas, which subsequently lead to impulsive stabilization heuristics that are amenable to implementation in a scientific computing environment. Two examples are provided to illustrate the results.