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On robustness of exact controllability and exact observability under cross perturbations of the generator in Banach spaces


Authors: Zhan-Dong Mei and Ji-Gen Peng
Journal: Proc. Amer. Math. Soc. 138 (2010), 4455-4468
MSC (2010): Primary 93C25, 93B05, 93B07
Published electronically: July 19, 2010
MathSciNet review: 2680070
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2010-10499-9
Keywords: $C_{0}$-semigroup, cross perturbation, admissibility, robustness, exact controllability, exact observability.
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.