Abstract
It is known that ifA is a normal reductive linear operator on a Hilbert space and the linear system {A, B} is controllable, then there exists a vectorb in the range ofB such that {A, B} is controllable. It is shown that this result does not hold for an arbitrary normal operatorA.
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Research partiablly supported by the National Science Foundation.
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Lubin, A.R. A note on single input controllability for normal systems. Math. Systems Theory 15, 371–373 (1981). https://doi.org/10.1007/BF01786992
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DOI: https://doi.org/10.1007/BF01786992