The asymptotical stability of a dynamic system uppercasewith structural damping

Xuezhang Hou

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 2, page 131-138
  • ISSN: 1641-876X

Abstract

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A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.

How to cite

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Hou, Xuezhang. "The asymptotical stability of a dynamic system uppercasewith structural damping." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 131-138. <http://eudml.org/doc/207628>.

@article{Hou2003,
abstract = {A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.},
author = {Hou, Xuezhang},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {dynamic system; asymptotic stability; evolution equation; exponential stability; beam equation; abstract evolution equation},
language = {eng},
number = {2},
pages = {131-138},
title = {The asymptotical stability of a dynamic system uppercasewith structural damping},
url = {http://eudml.org/doc/207628},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Hou, Xuezhang
TI - The asymptotical stability of a dynamic system uppercasewith structural damping
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 2
SP - 131
EP - 138
AB - A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.
LA - eng
KW - dynamic system; asymptotic stability; evolution equation; exponential stability; beam equation; abstract evolution equation
UR - http://eudml.org/doc/207628
ER -

References

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  1. Hou X. and Tsui S.-K. (2000): Control and stability of a torsional elastic robot arm. - J. Math. Anal.Appl., Vol. 243, pp. 140-162. Zbl0979.93055
  2. Hou X. and Tsui S.-K. (1999): A mathematical model for flexible robot arms system modelling and optimization, In: Chapman and Hall CRC Res. Notes Math. - Boca Raton FL: Chapman and Hall CRC, Vol. 396, pp. 391-398. Zbl0928.93040
  3. Hou X. and Tsui S.-K. (1998): A control theory for Cartesian flexible robot arms. - J. Math. Anal. Appl., Vol. 225, pp. 265-288. Zbl0927.93037
  4. Hou X. and Tsui S.-K. (2003): A feedback control and simulation for a flexible robot arm. - J. Appl. Math. Comp., Vol. 142, No. 2-3, pp. 389-407. Zbl1127.93331
  5. Komkov V. (1978): Control theory variational principles and optimal design of elastic systems, In: Optimal Control and Differential Equations. - New York: Academic Press, pp. 35-40. Zbl0453.49030
  6. Li S. and Zhu G. (1988): A property of the C_0-semigroup corresponding to the slender flying vehicle system with structural damp. - J. Syst. Sci. Math. Sci., Vol. 8, No. 3, pp. 219-225. Zbl0654.47022
  7. Kohne M. (1978): The control of vibrating elastic systems in control and systems theory. - Distributed parameter systems, Vol. 6, pp. 388-456. 
  8. Pazy A. (1983): Semigroups of Linear Operators and Applications to Partial Differential Equaitons. - New York: Spinger-Verlag. Zbl0516.47023
  9. Balaskrishnan A.V. (1981): Applied Functional Analysis. -New York: Springer-Verlag. 

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