Feedback invariants of restrictions -- a polynomial approach (Q5926166)
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scientific article; zbMATH DE number 1570701
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Feedback invariants of restrictions -- a polynomial approach |
scientific article; zbMATH DE number 1570701 |
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Feedback invariants of restrictions -- a polynomial approach (English)
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28 February 2001
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matrix polynomial representation
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feedback equivalence
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controllability indices
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Hermite indices
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The aim of this paper is to study the following problem. Under what conditions does there exist a matrix \(X\) such that the system NEWLINE\[NEWLINE\left(\left[\begin{matrix} A_1 A& X\\ 0 & A_2\end{matrix}\right], \left[\begin{matrix} 0\\ B_2\end{matrix}\right]\right)NEWLINE\]NEWLINE is in a given feedback equivalence class? Here \(A_1\), \(A_2\) and \(B_2\) known matrices, and \((A_2, B_2)\) is a controllable pair. Since the equivalence classes are characterized by the controllability indices, the problem is rewritten into a question where controllability indices are prescribed. However, for a solution this problem needs to be relaxed to a question in which the Hermite indices are prescribed.
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