Complete Controllability and Spectrum Assignment in Infinite Dimensional Spaces

Aleksander Markus and Vadim Olshevsky

The concept of complete controllability of a system plays an important role in the theory of systems with control. A large number of conditions is known, which are equivalent to complete controllability. Some of these are generalized to infinite dimensional case.

In the present paper two further criteria for complete controllability in infinite dimensional spaces are derived. We also obtained a new proof for the recent Takahashi theorem on the equivalence in Hilbert spaces of complete controllability and the assignability of the spectrum.

Examples are presented which show that in Banach spaces the assignability of the spectrum does not always follow from complete controllability. Properties which are dual to complete controllability are investigated in this paper as well. They can be applied to the study of observability in infinite dimensional spaces. Finally, the connections with the theory of analytic operator functions are indicated.

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Last modified: Fri Sep 15 1995