文章基本信息

标题：Strong stabilization of small water waves in a pool ⁎ ⁎
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作者：Pei Su ; Marius Tucsnak ; George Weiss 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：9
页码：378-383
DOI：10.1016/j.ifacol.2021.06.096
语种：English
出版社：Elsevier
摘要：AbstractThis paper is about the strong stabilization of small amplitude gravity water waves in a vertical rectangle. The control imposes the horizontal acceleration of the water along one vertical boundary segment, as a multiple of a scalar input functionu,times a functionhof the position along the active boundary. The statezof the system is a vector with two components: one is the water levelζalong the top boundary and the other is its time derivative ζ. We prove that for suitable functionsh,there exists a bounded feedback functionalFsuch that the feedbacku=Fzleads to a strongly stable closed-loop system. Moreover, for initial states in the domain of the semigroup generator, the norm of the solution decays like (1 + t) − 1/6. Our approach uses careful estimates on certain partial Dirichlet to Neumann and Neumann to Neumann operators associated to the rectangular domain, as well as non-uniform stabilization results due to Chill, Paunonen, Seifert, Stahn and Tomilov (2019).
关键词：KeywordsLinearized water waves equationcollocated actuatorssensorsDirichlet to Neumann mapNeumann to Neumann mapstrong stabilization