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Linear feedback systems and the groups of Galois and Lie. (English) Zbl 0509.93049

MSC:
93D15 Stabilization of systems by feedback
93C05 Linear systems in control theory
12E05 Polynomials in general fields (irreducibility, etc.)
22E60 Lie algebras of Lie groups
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[1] Evans, W.R., Graphical analysis of control systems, Trans. AIEE, 67, 547-551, (1948)
[2] Brockett, R.W.; Rahimi, A., Lie algebras and linear differential equations, (), 379-386
[3] Brockett, R.W., The Lie groups of simple feedback systems, IEEE decision and control conference, 1189-1193, (1976)
[4] Brockett, R.W., Lie algebras and rational functions: some control theoretic connections, (), 268-280
[5] Brockett, R.W., Polynomials, bilinear forms, and representations of Lie algebras, (), 1-6, AMS Lectures on Applied Mathematics
[6] Cartan, E., LES groupes de transformations continus, infinis, simples, Ann. √©cole norm. sup., 26, 93-161, (1909) · JFM 40.0193.02
[7] Kobayashi, S.; Nagumo, T., On filtered Lie algebras and geometric structures, J. math. and mech., 4, 679-706, (1965) · Zbl 0163.28103
[8] Singer, I.M.; Sternberg, S., On the infinite groups of Lie and Cartan, I, J. analyse math., XV, 1-114, (1965) · Zbl 0277.58008
[9] Guillemin, V.W.; Quillen, D.; Sternberg, S., The classification of the irreducible complex algebras of the infinite type, J. analyse math., 18, 107-112, (1967) · Zbl 0153.05903
[10] Kostant, B., A characterization of the classical groups, Duke math. J., 25, 107-123, (1951) · Zbl 0079.04301
[11] Byrnes, C.I.; Stevens, P.K., Global properties of the root-locus map, (), Lecture Notes in Information and Control · Zbl 0479.93021
[12] Adler, M.; van Moerbeke, P., Completely integrable systems, Euclidean Lie algebras, and curves, Adv. in math., 39, 267-317, (1980) · Zbl 0455.58017
[13] Jacobson, N., Basic algebra 1, (1974), Freeman San Francisco
[14] S. Friedland, Simultaneous similarity of matrices, Advances in Math, to appear. · Zbl 0527.15005
[15] Freudenthal, H., Elementarteilertheorie der komplexen orthognalen und symplektischen gruppen, Nederl. akad. wetensch. indag. math., 14, 99-101, (1952)
[16] Harris, J., Galois groups of enumerative problems, Duke math. J., 46, 685-724, (1979) · Zbl 0433.14040
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