The Riesz basis property of discrete operators and application to a Euler-Bernoulli beam equation with boundary linear feedback control

Authors:
  • BGBao‐Zhu Guo
    Bao‐Zhu Guo
  • RYRunyi Yu
    Runyi Yu
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Abstract
In this paper, we give an abstract condition of Riesz basis generation for discrete operators in Hilbert spaces, from which we show that the generalized eigenfunctions of a Euler–Bernoulli beam equation with boundary linear feedback control form a Riesz basis for the state Hilbert space. As an consequence, the asymptotic expression of eigenvalues together with exponential stability are readily presented.