On robustness of exact controllability and exact observability under cross perturbations of the generator in Banach spaces
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Abstract:
This paper is concerned with the exact controllability and exact observability of linear systems in the Banach space setting. It is proved that both the admissibility of control operators and the admissibility of observation operators are invariant to cross perturbations of the generator of a $C_0$-semigroup. Moreover, under the admissibility invariance premise, the robustness of the exact controllability as well as the exact observability to such cross perturbations is verified. An illustrative example is presented.References
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Additional Information
- Zhan-Dong Mei
- Affiliation: Department of Mathematics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
- Email: mzhd1516@gmail.com
- Ji-Gen Peng
- Affiliation: Department of Mathematics, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
- Email: jgpeng@mail.xjtu.edu.cn
- Received by editor(s): November 27, 2009
- Received by editor(s) in revised form: February 4, 2010, and March 12, 2010
- Published electronically: July 19, 2010
- Additional Notes: This work was supported by the Natural Science Foundation of China under contract No. 60970149
- Communicated by: Nigel J. Kalton
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 4455-4468
- MSC (2010): Primary 93C25, 93B05, 93B07
- DOI: https://doi.org/10.1090/S0002-9939-2010-10499-9
- MathSciNet review: 2680070