Riesz Basis Approach to the Stabilization of a Flexible Beam with a Tip Mass

Authors:
Bao-Zhu Guo
Affiliations:
-
Venue:
SIAM Journal on Control and Optimization
Year:
2000

Citing 0
Cited 4

On Spectrum of a General Petrovsky Type Equation and Riesz Basis of N-Connected Beams with Linear Feedback at Joints

Journal of Dynamical and Control Systems
A Hybrid Symbolic-Numerical Simulation Method for Some Typical Boundary Control Problems

Simulation
Optimal Energy Decay for a Nonhomogeneous Flexible Beam with a Tip Mass

Journal of Dynamical and Control Systems
Output-Feedback Stabilization of an Anti-stable Schrödinger Equation by Boundary Feedback with Only Displacement Observation

Journal of Dynamical and Control Systems

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Abstract

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 [ SIAM J. Control Optim., 36 (1998), pp. 1962--1986] are concluded as a special case, and the additional conditions imposed there are removed.