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Feedback equivalence of constant linear systems. (English) Zbl 0628.93007
Let O(A,B) be the orbit of the feedback equivalence (A,B)\(\approx (S(A+BT^{-1}K)S^{-1},SBT^{-1})\) of pairs of matrices. The author establishes criteria for \(O(A,B)=O(A',B')\) and O(A’,B’)\(\subset \overline{O(A,B)}\) in terms of Kronecker indices of the pairs and relates his result to the Gerstenhaber-Hesse-link theorem [M. Gerstenhaber, Ann. Math., II. Ser. 70, 167-205 (1959; Zbl 0168.281)].
Reviewer: P.Brunovsky

MSC:
93B10 Canonical structure
15A21 Canonical forms, reductions, classification
93C05 Linear systems in control theory
93B05 Controllability
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References:
[1] Brunovsky, P.A.A., A classification of linear controllable systems, Kybernetica (praha), 3, 173-187, (1970) · Zbl 0199.48202
[2] Gerstenhaber, M., On nilalgebras and linear varieties of nilpotent matrices, III, Annals of math., 70, 167-205, (1959) · Zbl 0168.28103
[3] Hazewinkel, M.; Martin, C.F., Representations of the symmetric group, the specialization order, systems and grassman manifolds, Enseign. math., 29, 53-87, (1983) · Zbl 0536.20009
[4] Kalman, R.E., Kronecker invariants and feedback (+ errata), (), 459-471 · Zbl 0308.93008
[5] Tannenbaum, A., Invariance and system theory: algebraic and geometric aspects, () · Zbl 0456.93001
[6] Wonham, W.A.; Morse, A.S., Feedback invariants of linear multivariable systems, Automatica, 8, 93-100, (1972) · Zbl 0235.93007
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