Abstract

In this paper, we consider a dynamic feedback problem of a pendulum coupled with a viscous damped wave equation. We show that the system operator generates a C 0 -semigroup of contractions in the energy state space, and the system is well-posed. By giving the asymptotic expressions of the eigenvalues of the system, we know that they all locate in the left hand side of the complex plane. It follows that the C 0 -semigroup generated by the system operator achieves strong stability when the feedback gain is real.

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