文章基本信息

标题：Stabilization of the linear Kuramoto-Sivashinsky equation with a delayed boundary control
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作者：Patricio Guzmán ; Swann Marx ; Eduardo Cerpa 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2019
卷号：52
期号：2
页码：70-75
DOI：10.1016/j.ifacol.2019.08.013
语种：English
出版社：Elsevier
摘要：AbstractIn this paper we stabilize the linear Kuramoto-Sivashinsky equation by means of a delayed boundary control. From the spectral decomposition of the spatial operator associated to the equation, we find that there is a finite number of unstable eigenvalues. After applying the Artstein transform to deal with the delay phenomenon, we design a feedback law based on the pole-shifting theorem to exponential stabilize the finite-dimensional system associated to the unstable eigenvalues. Then, thanks to the use of a Lyapunov function, we prove that the same feedback law exponential stabilize the original unstable infinite-dimensional system.
关键词：KeywordsPartial differential equationstime delayglobal stabilityfeedback stabilizationtransformationspole assignmentLyapunov function