Existence and Exponential Stability for a Euler-Bernoulli Beam Equation with Memory and Boundary Output Feedback Control Term

2008 ◽  
Vol 104 (3) ◽  
pp. 287-301 ◽  
Author(s):  
Jong Yeoul Park ◽  
Yong Han Kang ◽  
Jung Ae Kim
Keyword(s):  
Feedback Control ◽  
Exponential Stability ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam ◽  
With Memory

scholarly journals The Exponential Stability Result of an Euler-Bernoulli Beam Equation with Interior Delays and Boundary Damping

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Peng-cheng Han ◽  
Yan-fang Li ◽  
Gen-qi Xu ◽  
Dan-hong Liu
Keyword(s):  
Exponential Stability ◽  
Semigroup Theory ◽  
Stability Result ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Boundary Damping ◽  
Exponentially Stable ◽  
Stability Issue ◽  
Euler Bernoulli Beam ◽  
The Relationship

We study the exponential stability of Euler-Bernoulli beam with interior time delays and boundary damping. At first, we prove the well-posedness of the system by the C0 semigroup theory. Next we study the exponential stability of the system by constructing appropriate Lyapunov functionals. We transform the exponential stability issue into the solvability of inequality equations. By analyzing the relationship between delays parameters α and damping parameters β, we describe (β,α)-region for which the system is exponentially stable. Furthermore, we obtain an estimation of the decay rate λ⁎.

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