Well-posedness and regularity of Euler–Bernoulli equation with variable coefficient and Dirichlet boundary control and collocated observation
نویسندگان
چکیده
Two types of open-loop systems of an Euler–Bernoulli equation with variable coefficient and Dirichlet boundary control and collocated observation are considered. The uncontrolled boundary is either hinged or clamped. It is shown, with the help of multiplier method on Riemannian manifold, that in both cases, systems are well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. In addition, the feedthrough operators are found to be zero. The result implies that the exact controllability of open-loop is equivalent to the exponential stability of closed-loop under a proportional output feedback for these systems. Copyright © 2013 John Wiley & Sons, Ltd.
منابع مشابه
Well-posedness and regularity for an Euler-Bernoulli plate with variable coefficients and boundary control and observation
The open loop system of an Euler–Bernoulli plate with variable coefficients and partial boundary Neumann control and collocated observation is considered. Using the geometric multiplier method on Riemannian manifolds, we show that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. Moreover, we determine that the feedthrough operator of this system is zero....
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