scholarly journals Exponential stability of variable coefficients Rayleigh beams under boundary feedback controls: a Riesz basis approach

2004 ◽  
Vol 51 (1) ◽  
pp. 33-50 ◽  
Author(s):  
Jun-min Wang ◽  
Gen-qi Xu ◽  
Siu-Pang Yung
Keyword(s):  
Exponential Stability ◽  
Riesz Basis ◽  
Variable Coefficients ◽  
Feedback Controls ◽  
Boundary Feedback

scholarly journals Stabilization of Variable Coefficients Euler-Bernoulli Beam with Viscous Damping under a Force Control in Rotation and Velocity Rotation

2017 ◽  
Vol 9 (6) ◽  
pp. 1
Author(s):  
Bomisso G. Jean Marc ◽  
Tour\'{e} K. Augustin ◽  
Yoro Gozo
Keyword(s):  
Exponential Stability ◽  
Force Control ◽  
Riesz Basis ◽  
Closed Loop ◽  
Variable Coefficients ◽  
Viscous Damping ◽  
Closed Loop System ◽  
Bernoulli Beam ◽  
Spectral System ◽  
Euler Bernoulli Beam

This paper investigates the problem of exponential stability for a damped Euler-Bernoulli beam with variable coefficients clamped at one end and subjected to a force control in rotation and velocity rotation. We adopt the Riesz basis approach for show that the closed-loop system is a Riesz spectral system. Therefore, the exponential stability and the spectrum-determined growth condition are obtained.

Exponential stability of string system with variable coefficients under non-collocated feedback controls

2010 ◽  
Vol 13 (1) ◽  
pp. 148-163 ◽  
Author(s):  
Yunlan Chen ◽  
Zhongjie Han ◽  
Genqi Xu ◽  
Dongyi Liu
Keyword(s):  
Exponential Stability ◽  
Variable Coefficients ◽  
Feedback Controls

scholarly journals Riesz basis property and exponential stability for one-dimensional thermoelastic system with variable coefficients

2021 ◽  
Author(s):  
Bao-Zhu Guo ◽  
Han-Jing Ren
Keyword(s):  
Exponential Stability ◽  
Riesz Basis ◽  
Basis Property ◽  
Coupled System ◽  
Variable Coefficients ◽  
Operator Pencil ◽  
Riesz Basis Property ◽  
Asymptotic Expressions ◽  
The Matrix ◽  
Constant Coefficients

In this paper, we study Riesz basis property and stability for a nonuniform thermoelastic system with Dirichlet-Dirichlet boundary condition, where the  heat subsystem is considered as a control to the whole coupled system. By means of the matrix operator pencil method, we obtain the asymptotic expressions of the eigenpairs, which are exactly coincident to the constant coefficients case} We then show that there exists a sequence of generalized eigenfunctions of the system,  which forms a Riesz basis for the state space and the spectrum determined growth condition is therefore proved. As a result, the exponential stability of the system is concluded.

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