# zbMATH — the first resource for mathematics

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
Full Text:
##### 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.