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Control systems on Lie groups. (English) Zbl 0237.93027


MSC:

93C25 Control/observation systems in abstract spaces
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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References:

[1] Brockett, R. W., System theory on group manifolds and coset spaces, SIAM J. Control (1972), to appear in · Zbl 0238.93001
[2] Chevalley, C., Theory of Lie Groups (1946), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0063.00842
[3] Haynes, G. W.; Hermes, H., Nonlinear controllability via Lie theory, SIAM J. Control, 8, 450-460 (1970) · Zbl 0229.93012
[4] Helgason, S., Differential Geometry and Symmetric Spaces (1962), Academic Press: Academic Press New York · Zbl 0122.39901
[5] Kobayashi, S.; Nomizu, K., (Foundations of Differential Geometry, Vol. 1 (1963), Interscience: Interscience New York) · Zbl 0119.37502
[6] Kučera, J., Solution in large of control problem: \(ẋ = (A(1 − u) + Bu)x\), Czech. Math. J., 16, 600-623 (1966) · Zbl 0207.46902
[7] Kučera, J., Solution in large of control problem: \(ẋ = (Au + Bv)x\), Czech. Math. J., 17, 91-96 (1967) · Zbl 0189.15701
[8] Lobry, C., Contrôlabilité des systèmes non linéaires, SIAM J. Control, 8, 573-605 (1970) · Zbl 0207.15201
[9] Sternberg, S., Lectures on Differential Geometry (1964), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0129.13102
[10] H. J. Sussmann\( GL nR\)SIAM J. Control; H. J. Sussmann\( GL nR\)SIAM J. Control
[11] H. J. Sussmann and V. JurdjevicJ. Differential Eq.; H. J. Sussmann and V. JurdjevicJ. Differential Eq. · Zbl 0227.93011
[12] Yamabe, H., On an arcwise connected subgroup of a Lie group, Osaka Math. J., 13-14 (1950) · Zbl 0039.02101
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