Sussmann, Hector J.; Jurdjevic, Velimir Controllability of nonlinear systems. (English) Zbl 0242.49040 J. Differ. Equations 12, 95-116 (1972). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 175 Documents MSC: 93B03 Attainable sets, reachability 93B05 Controllability PDF BibTeX XML Cite \textit{H. J. Sussmann} and \textit{V. Jurdjevic}, J. Differ. Equations 12, 95--116 (1972; Zbl 0242.49040) Full Text: DOI OpenURL References: [1] Bishop, R.L; Crittenden, R.J, Geometry of manifolds, (1964), Academic Press New York · Zbl 0132.16003 [2] {\scR. W. Brockett}, System theory on group manifolds and coset spaces, SIAM J. Control, to appear. · Zbl 0238.93001 [3] Chevalley, C, Theory of Lie groups, (1946), Princeton University Press Princeton, NJ · Zbl 0063.00842 [4] Chow, W.L, Über systeme von linearen partiellen differential-gleichungen erster ordnung, Math. ann., 117, 98-105, (1939) · Zbl 0022.02304 [5] Elliott, D.L, A consequence of controllability, J. diff. eqs., 10, 364-370, (1971) · Zbl 0216.27502 [6] Haynes, G.W; Hermes, H, Nonlinear controllability via Lie theory, SIAM J. control, 8, 450-460, (1970) · Zbl 0229.93012 [7] Helgason, S, Differential geometry and symmetric spaces, (1962), Academic Press New York · Zbl 0122.39901 [8] Hermann, R, E. Cartan’s geometric theory of partial differential equations, Advances in math., 1, 265-315, (1965) · Zbl 0142.07104 [9] Hermann, R, On the accessibility problem in control theory, (), 325-332 [10] Hermann, R, The differential geometry of foliations II, J. math. mech., 11, 305-315, (1962) · Zbl 0152.20502 [11] Jurdjevic, V, Abstract control systems: controllability and observability, SIAM J. control, 8, 424-439, (1970) · Zbl 0262.93006 [12] Kalman, R.E; Ho, Y.C; Narendra, K.S, Controllability of linear dynamical systems, Contrib. diff. eqs., 1, 189-213, (1963) · Zbl 0151.13303 [13] Kobayashi, S; Nomizu, K, () [14] Kučera, J, Solution in large of control problem: ẋ = (A(1 − u) + bu)x, Czech. math. J., 16, 91, 600-623, (1966) · Zbl 0207.46902 [15] Kučera, J, Solution in large of control problem: ẋ = (au + bv)x, Czech. math. J., 17, 92, 91-96, (1967) · Zbl 0189.15701 [16] Lobry, C, Contrôlabilité des systèmes non linéaires, SIAM J. control, 8, 573-605, (1970) · Zbl 0207.15201 [17] Lobry, C, Une propriété de l’ensemble des états accessibles d’un système guidable, C. R. acad. sci. Paris, 272, 153-156, (1971), Series A · Zbl 0207.15202 [18] Spanier, E.H, Algebraic topology, (1966), McGraw-Hill New York · Zbl 0145.43303 [19] Sternberg, S, Lectures on differential geometry, (1964), Prentice Hall Englewood Cliffs, NJ · Zbl 0129.13102 [20] {\scH. J. Sussmann}, The bang-bang problem for certain control systems in GL(n, R), SIAM J. Control, to appear. [21] {\scH. J. Sussmann}, The control problem ẋ = (A(1 − u) + Bu)x: a comment on an article by J. Kučera, Czec · Zbl 0251.49014 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.