A note on the boundary stabilization of an axially moving elastic tape
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We consider a linear Euler–Bernoulli beam equation introduced by Russell (Appl Math Optim 46:291–312, 2002) that equation describes the motion of a tape moving axially between two sets of rollers. We discuss an underlying hybrid model accounting for the mass of the roller assembly and show that the system is uniformly stable; this result generalizes an earlier result by Russell and Liu (Control theory of partial differential equations, Lecture Notes Pure and Applied Mathematics, vol 242, Chapman and Hall/CRC, Boca Raton, pp 183–194, 2005), where the mass of the rollers is neglected. The proof of our well-posedness and stabilization result shows in particular that if the mass is also neglected, then no boundary controls are needed to achieve the exponential stability of the system, which improves the exponential stability result in Russell and Liu (2005) where a force control is needed.
KeywordsAxially moving beam Boundary stabilization Hybrid system
Mathematics Subject Classification93D15 35B35 35Q74
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