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Exponential stability of perturbed superstable systems in Hilbert spaces |
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| Authors: | |
| Institution: | 1.School of Mathematics and Computational Science,Hunan University of Science and Technology,Xiangtan,People’s Republic of China;2.School of Mathematics and Computational Science,Xiangtan University,Xiangtan,People’s Republic of China;3.School of Physics and Optoelectronic Engineering,Foshan University,Foshan,People’s Republic of China |
| Abstract: | We study exponential stability of superstable systems in Hilbert spaces under perturbations. Formulas to calculate or to estimate the exponential growth bound of the perturbed systems are derived via which sufficient conditions on exponential stability are established. The obtained results are applied to a partial differential equation governing the vibration of a smart beam made of self-straining material. Several numerical simulations are given. |
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