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1. | Institut universitaire de France and Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France |
References:
[1] |
Karine Beauchard, Jean Michel Coron, Mazyar Mirrahimi and Pierre Rouchon, Implicit lyapunov control of finite dimensional schrödinger equations, Systems Control Lett., 56 (2007), 388-395.
doi: 10.1016/j.sysconle.2006.10.024. |
[2] |
Sanjay P. Bhat and Dennis S. Bernstein, Geometric homogeneity with applications to finite-time stability, Math. Control Signals Systems, 17 (2005), 101-127.
doi: 10.1007/s00498-005-0151-x. |
[3] |
Bernard Bonnard, Contrôlabilité de systemes mécaniques sur les groupes de lie, (French) [Controllability of mechanical systems on Lie groups] SIAM J. Control Optim., 22 (1984), 711-722.
doi: 10.1137/0322045. |
[4] |
Bernard Bonnard, Ludovic Faubourg and Emmanuel Trélat, "Mécanique CÉleste Et Contrôle Des VÉhicules Spatiaux," (French) [Celestial mechanics and the control of space vehicles] Mathématiques & Applications (Berlin) [Mathematics & Applications], Springer-Verlag, Berlin, 2006. |
[5] |
Christopher I. Byrnes and Alberto Isidori, New results and examples in nonlinear feedback stabilization, Systems Control Lett., 12 (1989), 437-442.
doi: 10.1016/0167-6911(89)90080-7. |
[6] |
Jean-Michel Coron, On the controllability of $2$-D incompressible perfect fluids, J. Math. Pures Appl., 75 (1996), 155-188. |
[7] |
Jean-Michel Coron, On the null asymptotic stabilization of the two-dimensional incompressible euler equations in a simply connected domain, SIAM J. Control Optim., 37 (1999), 1874-1896.
doi: 10.1137/S036301299834140X. |
[8] |
Jean-Michel Coron, Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, A tribute to J. L. Lions. ESAIM Control Optim. Calc. Var., 8 (2002), 513-554.
doi: 10.1051/cocv:2002050. |
[9] |
Jean-Michel Coron, "Control and Nonlinearity," Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007. |
[10] |
Jean-Michel Coron, On the controllability of nonlinear partial differential equations, In "Proceedings of the International Congress of Mathematicians. Volume I," pages 238-264, Hindustan Book Agency, New Delhi, 2010. |
[11] |
Wijesuriya P. Dayawansa, Clyde F. Martin and Sandra L. Samelson Samelson, Asymptotic stabilization of a generic class of three-dimensional homogeneous quadratic systems, Systems Control Lett., 24 (1995), 115-123.
doi: 10.1016/0167-6911(94)00040-3. |
[12] |
Ludovic Faubourg and Jean-Baptiste Pomet, Control lyapunov functions for homogeneous "Jurdjevic-Quinn'' systems, ESAIM Control Optim. Calc. Var., 5 (2000), 293-311(electronic).
doi: 10.1051/cocv:2000112. |
[13] |
Olivier Glass, Exact boundary controllability of 3-D euler equation, ESAIM Control Optim. Calc. Var., 5 (2000), 1-44 (electronic).
doi: 10.1051/cocv:2000100. |
[14] |
Olivier Glass, Asymptotic stabilizability by stationary feedback of the two-dimensional euler equation: The multiconnected case, SIAM J. Control Optim., 44 (2005), 1105-1147 (electronic).
doi: 10.1137/S0363012903431153. |
[15] |
Andreea Grigoriu, Implicit lyapunov control for schrödinger equations with dipole and polarizability term, Proc. of the 50th IEEE Conf. on Decision and Control, USA, December 2011. |
[16] |
Henry Hermes, Homogeneous coordinates and continuous asymptotically stabilizing feedback controls, In "Differential Equations" (Colorado Springs, CO, 1989), Lecture Notes in Pure and Appl. Math., pages 249-260. Dekker, New York, 1991. |
[17] |
Henry Hermes, Smooth homogeneous asymptotically stabilizing feedback controls, ESAIM Control Optim. Calc. Var., 2 (1997), 13-32 (electronic).
doi: 10.1051/cocv:1997101. |
[18] |
Hamadi Jerbi, On the stabilizability of homogeneous systems of odd degree, ESAIM Control Optim. Calc. Var., 9 (2003), 343-352 (electronic).
doi: 10.1051/cocv:2003016. |
[19] |
Hassan K. Khalil, "Nonlinear Systems," Prentice Hall, New Jersey, 2002.
doi: 10.1007/s11071-008-9349-z. |
[20] |
Daniel E. Koditschek, Adaptive techniques for mechanical systems, In "Proc. 5th. Yale University Conference, New Haven" (1987), pages 259-265. Yale University, New Haven, 1987. |
[21] |
Pascal Morin, Jean-Baptiste Pomet and Claude Samson, Design of homogeneous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of lie brackets in closed loop, SIAM J. Control Optim., 38 (1999), 22-49 (electronic).
doi: 10.1137/S0363012997315427. |
[22] |
Pascal Morin and Claude Samson, Time-varying exponential stabilization of a rigid spacecraft with two control torques, IEEE Trans. Automat. Control, 42 (1997), 528-534.
doi: 10.1109/9.566663. |
[23] |
Laurent Praly, Brigitte d'Andréa-Novel and Jean-Michel Coron, Lyapunov design of stabilizing controllers for cascaded systems, IEEE Trans. Automat. Control, 36 (1991), 1177-1181.
doi: 10.1109/9.90230. |
[24] |
Lionel Rosier, Homogeneous lyapunov function for homogeneous continuous vector fields, Systems Control Lett., 19 (1992), 467-473.
doi: 10.1016/0167-6911(92)90078-7. |
[25] |
Eduardo D. Sontag, "Mathematical Control Theory," Deterministic finite-dimensional systems, Second edition, Texts in Applied Mathematics, Springer-Verlag, New York, 1998. |
[26] |
John Tsinias, Sufficient Lyapunov-like conditions for stabilization, Math. Control Signals Systems, 2 (1989), 343-357.
doi: 10.1007/BF02551276. |
show all references
References:
[1] |
Karine Beauchard, Jean Michel Coron, Mazyar Mirrahimi and Pierre Rouchon, Implicit lyapunov control of finite dimensional schrödinger equations, Systems Control Lett., 56 (2007), 388-395.
doi: 10.1016/j.sysconle.2006.10.024. |
[2] |
Sanjay P. Bhat and Dennis S. Bernstein, Geometric homogeneity with applications to finite-time stability, Math. Control Signals Systems, 17 (2005), 101-127.
doi: 10.1007/s00498-005-0151-x. |
[3] |
Bernard Bonnard, Contrôlabilité de systemes mécaniques sur les groupes de lie, (French) [Controllability of mechanical systems on Lie groups] SIAM J. Control Optim., 22 (1984), 711-722.
doi: 10.1137/0322045. |
[4] |
Bernard Bonnard, Ludovic Faubourg and Emmanuel Trélat, "Mécanique CÉleste Et Contrôle Des VÉhicules Spatiaux," (French) [Celestial mechanics and the control of space vehicles] Mathématiques & Applications (Berlin) [Mathematics & Applications], Springer-Verlag, Berlin, 2006. |
[5] |
Christopher I. Byrnes and Alberto Isidori, New results and examples in nonlinear feedback stabilization, Systems Control Lett., 12 (1989), 437-442.
doi: 10.1016/0167-6911(89)90080-7. |
[6] |
Jean-Michel Coron, On the controllability of $2$-D incompressible perfect fluids, J. Math. Pures Appl., 75 (1996), 155-188. |
[7] |
Jean-Michel Coron, On the null asymptotic stabilization of the two-dimensional incompressible euler equations in a simply connected domain, SIAM J. Control Optim., 37 (1999), 1874-1896.
doi: 10.1137/S036301299834140X. |
[8] |
Jean-Michel Coron, Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, A tribute to J. L. Lions. ESAIM Control Optim. Calc. Var., 8 (2002), 513-554.
doi: 10.1051/cocv:2002050. |
[9] |
Jean-Michel Coron, "Control and Nonlinearity," Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2007. |
[10] |
Jean-Michel Coron, On the controllability of nonlinear partial differential equations, In "Proceedings of the International Congress of Mathematicians. Volume I," pages 238-264, Hindustan Book Agency, New Delhi, 2010. |
[11] |
Wijesuriya P. Dayawansa, Clyde F. Martin and Sandra L. Samelson Samelson, Asymptotic stabilization of a generic class of three-dimensional homogeneous quadratic systems, Systems Control Lett., 24 (1995), 115-123.
doi: 10.1016/0167-6911(94)00040-3. |
[12] |
Ludovic Faubourg and Jean-Baptiste Pomet, Control lyapunov functions for homogeneous "Jurdjevic-Quinn'' systems, ESAIM Control Optim. Calc. Var., 5 (2000), 293-311(electronic).
doi: 10.1051/cocv:2000112. |
[13] |
Olivier Glass, Exact boundary controllability of 3-D euler equation, ESAIM Control Optim. Calc. Var., 5 (2000), 1-44 (electronic).
doi: 10.1051/cocv:2000100. |
[14] |
Olivier Glass, Asymptotic stabilizability by stationary feedback of the two-dimensional euler equation: The multiconnected case, SIAM J. Control Optim., 44 (2005), 1105-1147 (electronic).
doi: 10.1137/S0363012903431153. |
[15] |
Andreea Grigoriu, Implicit lyapunov control for schrödinger equations with dipole and polarizability term, Proc. of the 50th IEEE Conf. on Decision and Control, USA, December 2011. |
[16] |
Henry Hermes, Homogeneous coordinates and continuous asymptotically stabilizing feedback controls, In "Differential Equations" (Colorado Springs, CO, 1989), Lecture Notes in Pure and Appl. Math., pages 249-260. Dekker, New York, 1991. |
[17] |
Henry Hermes, Smooth homogeneous asymptotically stabilizing feedback controls, ESAIM Control Optim. Calc. Var., 2 (1997), 13-32 (electronic).
doi: 10.1051/cocv:1997101. |
[18] |
Hamadi Jerbi, On the stabilizability of homogeneous systems of odd degree, ESAIM Control Optim. Calc. Var., 9 (2003), 343-352 (electronic).
doi: 10.1051/cocv:2003016. |
[19] |
Hassan K. Khalil, "Nonlinear Systems," Prentice Hall, New Jersey, 2002.
doi: 10.1007/s11071-008-9349-z. |
[20] |
Daniel E. Koditschek, Adaptive techniques for mechanical systems, In "Proc. 5th. Yale University Conference, New Haven" (1987), pages 259-265. Yale University, New Haven, 1987. |
[21] |
Pascal Morin, Jean-Baptiste Pomet and Claude Samson, Design of homogeneous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of lie brackets in closed loop, SIAM J. Control Optim., 38 (1999), 22-49 (electronic).
doi: 10.1137/S0363012997315427. |
[22] |
Pascal Morin and Claude Samson, Time-varying exponential stabilization of a rigid spacecraft with two control torques, IEEE Trans. Automat. Control, 42 (1997), 528-534.
doi: 10.1109/9.566663. |
[23] |
Laurent Praly, Brigitte d'Andréa-Novel and Jean-Michel Coron, Lyapunov design of stabilizing controllers for cascaded systems, IEEE Trans. Automat. Control, 36 (1991), 1177-1181.
doi: 10.1109/9.90230. |
[24] |
Lionel Rosier, Homogeneous lyapunov function for homogeneous continuous vector fields, Systems Control Lett., 19 (1992), 467-473.
doi: 10.1016/0167-6911(92)90078-7. |
[25] |
Eduardo D. Sontag, "Mathematical Control Theory," Deterministic finite-dimensional systems, Second edition, Texts in Applied Mathematics, Springer-Verlag, New York, 1998. |
[26] |
John Tsinias, Sufficient Lyapunov-like conditions for stabilization, Math. Control Signals Systems, 2 (1989), 343-357.
doi: 10.1007/BF02551276. |
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