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We consider the problem of boundary stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. This term puts all the eigenvalues of the open-loop system in the right half of the complex plane. We design a feedback law based on the backstepping method and prove exponential stability of the closed-loop system with a desired decay rate. For plants with constant...
The existence of a unique nonnegative time-dependent solution to the repairable system with N failure modes and one standby unit is obtained by using C0-semigroup theory. The spectral properties and the essential spectrum bound of the stand-by system are discussed by using perturbation method. In the end, we get the desired result that the dynamic solution of the system exponentially tends to the...
In this paper, the solution of a transfer line with a reliable machine, an unreliable machine and storage buffer is investigated. By using the method of functional analysis, especially, the linear operator theory on Banach space, we prove the existence of the strictly dominant eigenvalue, and show the linear stability and the exponential stability of solution.
In this paper we consider the dynamical stability of a tree-shape networks of Timoshenko beams with time-delay terms in the boundary controls. The time-delay feedback controllers at the exterior vertices are designed to derive the beams back to its equilibrium position. We first get the wellposedness of the closed loop system. Under certain conditions, we show that this system is asymptotically stable...
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