Abstract
The optimal decay rate problem is considered for boundary control system modeling by a flexible structure consisting of a Eular-Bernoulli beam. Controls are a bending moment in proportion to angular velocity and a shear force in proportion to velocity. A sensitivity asymptotic analysis of the system's eigenvalues and eigenfunctions is set up. It is proved that, for every 0<K 2<+∞ and 0<-K 1<+∞, all the generalized eigenfunctions of
form a Riesz basis ofV×H, and the optimal exponential decay rate can be obtained from the spectrum of the system.
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Project supported by the National Natural Science Foundation of China (Grant Nos. 69674011, 19671054) and Science Foundation of Shanxi University.
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Yu, J., Li, S., Wang, Y. et al. Optimal decay rate of vibrating beam equations controlled by combined boundary feedback forces. Sci. China Ser. E-Technol. Sci. 42, 354–364 (1999). https://doi.org/10.1007/BF02916744
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DOI: https://doi.org/10.1007/BF02916744