Exponential stabilization of a non-uniform porous-elasticity system

A kind of one-dimensional porous-elasticity system with variable coefficients is considered in this paper. The velocity of the solids at one end is observed. A feedback controller is designed to stabilize this system. By a complete spectral analysis, it is proved that the corresponding closed-loop s...

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Bibliographic Details
Main Authors: Zhong-Jie Han, Gen-Qi Xu, Xue-Guang Cao
Format: Conference Proceeding
Language:English
Subjects:
Asymptotic stability
Eigenvalues and eigenfunctions
Equations
Hilbert space
Mathematical model
Solids
Stability analysis
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Summary:A kind of one-dimensional porous-elasticity system with variable coefficients is considered in this paper. The velocity of the solids at one end is observed. A feedback controller is designed to stabilize this system. By a complete spectral analysis, it is proved that the corresponding closed-loop system satisfies the spectrum-determined-growth condition, that is, the decay rate of the system is determined by the spectral bound. Then the exponential stability is concluded based on the spectral distribution.