
Vietnam Journal of Mathematics 36:4(2008)
463472

Distance from an Exactly Controllable System
to Not Approximately Controllable Systems

B. T. Anh, D. C. Khanh,
and D. D. X. Thanh

Abstract. Given an exactly controllable
timeinvariant linear control system on a Hilbert space, the distance from
the given system to the set of not approximately controllable systems is
the norm of the smallest perturbation that makes the given system not approximately
controllable. In this paper, the distances when both or only one of the
system operators is perturbed are formulated in terms of optimization
problems depending on a complex variable. In some cases, these optimization
problems can be reduced to depend on one real variable, as well as the real
and complex radii are shown to be equal. The obtained results in this paper
also generalize the recent work of [6,12].


2000 Mathematics Subject Classification: 93B05, 93C25,
93C05.

Keywords: Controllability, timeinvariant linear
systems, distance, Hilbert spaces.


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by Vietnam Academy of Science and Technology & Vietnam Mathematical
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Published
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