On controllability of a non-homogeneous elastic string with memory

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• 作者：Sergei A. Avdonin ; Boris P. Belinskiy
• 关键词：Control for distributed parameter systems ; Elastic string ; Memory ; Duality principle ; Bases of functions ; Sobolev spaces
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2013
• 出版时间：1 February, 2013
• 年：2013
• 卷：398
• 期：1
• 页码：254-269
• 全文大小：302 K

文摘

We are motivated by the problem of control for a non-homogeneous elastic string with memory. We reduce the problem of controllability to a non-standard moment problem. The solution of the latter problem is based on an auxiliary Riesz basis property result for a family of functions quadratically close to the nonharmonic exponentials. This result requires the detailed analysis of an integro-differential equation and is of interest in itself for Function Theory. Controllability of the string implies observability of a dual system.