Abstract
The controllability indices are a complete system of invariants for the feedback equivalence relation of controllable matrix pairs. The Hermite indices are invariant for the similarity of matrix pairs but they are not invariant by changing basis on the input space and performing state feedback. The aim of this work is to partially characterize the Hermite indices of a controllable linear system, , when state feedback is performed on it. Namely, given a matrix pair (A, B), we study the problem of the existence of a matrix F such that (A+BF, B) has prescribed Hermite indices.
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