Vector Extensions of Halanay's Inequality

• 成果类型: Article
• 署名作者: Mazenc, Frederic; Malisoff, Michael; Krstic, Miroslav
• 署名单位: Louisiana State University System; Louisiana State University; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3062565
• 发表日期: 2022
• 页码: 1453-1459
• 关键词: convergence; DELAYS; asymptotic stability; Stability criteria; Time-varying systems; Lyapunov methods; Linear matrix inequalities; delay; Interval observer; STABILITY

摘要

We provide two extensions of Halanay's inequality, where the scalar function in the usual Halanay's inequality is replaced by a vector valued function, under a Metzler condition. We provide an easily checked necessary and sufficient condition for asymptotic convergence of the function to the zero vector in the time-invariant case. For the time-varying cases, we provide a sufficient condition for this convergence, which can be easily checked when the systems are periodic. We illustrate our results in cases that are beyond the scope of prior asymptotic stability results.