Guo, Bao-Zhu Riesz basis approach to the stabilization of a flexible beam with a tip mass. (English) Zbl 1183.93111 SIAM J. Control Optim. 39, No. 6, 1736-1747 (2001). Summary: Using an abstract condition of Riesz basis generation of discrete operators in the Hilbert spaces, we show, in this paper, that a sequence of generalized eigenfunctions of an Euler-Bernoulli beam equation with a tip mass under boundary linear feedback control forms a Riesz basis for the state Hilbert space. In the meanwhile, an asymptotic expression of eigenvalues and the exponential stability are readily obtained. The main results of F. Conrad, Ö. Morgül [SIAM J. Control Optimization 36, No. 6, 1962–1986 (1998; Zbl 0927.93031)] are concluded as a special case, and the additional conditions imposed there are removed. Cited in 64 Documents MSC: 93D15 Stabilization of systems by feedback 35B35 Stability in context of PDEs 35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs 93C20 Control/observation systems governed by partial differential equations Keywords:beam equation; boundary control; stability; eigenvalues; Riesz basis Citations:Zbl 0927.93031 PDFBibTeX XMLCite \textit{B.-Z. Guo}, SIAM J. Control Optim. 39, No. 6, 1736--1747 (2001; Zbl 1183.93111) Full Text: DOI