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

Mei, Zhan-Dong; Peng, Ji-Gen

doi:10.1090/S0002-9939-2010-10499-9

On robustness of exact controllability and exact observability under cross perturbations of the generator in Banach spaces
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Proc. Amer. Math. Soc. 138 (2010), 4455-4468 Request permission

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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