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

2001 ◽  
Vol 18 (2) ◽  
pp. 241-251 ◽  
Author(s):  
B.-Z. Guo
Keyword(s):  
Feedback Control ◽  
Riesz Basis ◽  
Basis Property ◽  
Linear Feedback ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Linear Feedback Control ◽  
Riesz Basis Property ◽  
Discrete Operators ◽  
Euler Bernoulli Beam

Riesz Basis Generation of the Euler-Bernoulli Beam Equation with Boundary Energy Dissipation

2012 ◽  
Vol 433-440 ◽  
pp. 123-127
Author(s):  
Cui Lian Zhou
Keyword(s):  
Energy Dissipation ◽  
Boundary Conditions ◽  
Riesz Basis ◽  
Boundary Energy ◽  
Basis Property ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Riesz Basis Property ◽  
Euler Bernoulli Beam ◽  
Regular Property

In this paper, the Riesz basis generation of the Euler-Bernoulli beam equation with with boundary energy dissipation is studied. Using the regular property of the boundary conditions, it is shown that the Riesz basis property holds

scholarly journals Riesz basis property of Timoshenko beams with boundary feedback control

2003 ◽  
Vol 2003 (28) ◽  
pp. 1807-1820 ◽  
Author(s):  
De-Xing Feng ◽  
Gen-Qi Xu ◽  
Siu-Pang Yung
Keyword(s):  
Feedback Control ◽  
Riesz Basis ◽  
Closed Loop ◽  
Loop System ◽  
Beam Equation ◽  
Closed Loop System ◽  
Boundary Feedback Control ◽  
Riesz Basis Property ◽  
Boundary Feedback ◽  
Generalized Eigenvectors

A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the state Hilbert space.

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