Discrete Ingham type inequalities and simultaneous observability of strings or beams

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• 作者：Vilmos Komornik ; Paola Loreti
• 关键词：Observability ; Fourier series ; Strings ; Beams
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2009
• 出版时间：1 March 2009
• 年：2009
• 卷：351
• 期：1
• 页码：16-28
• 全文大小：219 K

文摘

Harmonic analysis has been an efficient tool in control theory for a long time, see, e.g., Russell [D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. Recent progress and open questions, SIAM Rev. 20 (1978) 639–739] and its numerous references. Here we establish discrete Ingham type and Haraux type inequalities for exponential sums satisfying a weakened gap condition. They enable us to obtain discrete simultaneous observability theorems for systems of vibrating strings or beams.