Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernouilli beam with joint feedback control

• Autores: Bao-Zhu Guo, K. Y. Chan
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 14, Nº 1, 2001, págs. 205-230
• Idioma: inglés
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• Resumen

  • Using an abstract result on Riesz basis generation for discrete operators in general Hilbert spaces, we show, in this article, that the generalized eigenfunctions of an Euler-Bernoulli beam equation with joint linear feedback control form a Riesz basis for the state space. The spectrum-determined growth condition is hence obtained. Meanwhile, the exponential stability as well as the asymptotic expansion of eigenvalues are also readily obtained by a straightforward computation.