[1] Riccardo ADAMi et Ugo BoSCAiN : Controllability of the
Schrödinger equation via intersection of eigenvalues. In Proceedings
of the 44th IEEE Conference on Decision and Control, pages 1080-1085,
2005.
[2] Shmuel AGMoN : Bounds on exponential decay of
eigenfunctions of Schrödinger operators. In Schrödinger operators
(Como, 1984), volume 1159 de Lecture Notes in Math., pages 1- 38.
Springer, Berlin, 1985.
[3] Andrei AGRACHEv et Thomas CHAMBRioN : An estimation of
the controllability time for single-input systems on compact Lie groups.
ESAIM Control Optim. Calc. Var., 12(3):409- 441, 2006.
[4] Andrei A. AGRACHEv : A «Gauss-Bonnet formula» for
contact sub-Riemannian manifolds. Dokl. Akad. Nauk, 381(5):583-585,
2001.
[5] Andrei A. AGRACHEv et Daniel LiBERzoN : Lie-algebraic
stability criteria for switched systems. SIAM J. Control Optim.,
40(1):253-269, 2001.
[6] Andrei A. AGRACHEv et Yuri L. SACHKov : Control
theory from the geometric viewpoint, volume 87 de Encyclopaedia of
Mathematical Sciences. Springer-Verlag, Berlin, 2004. Control Theory and
Optimization, II.
[7] Andrey A. AGRACHEv et Andrey V. SARyCHEv : Controllability
of 2D Euler and NavierStokes equations by degenerate forcing. Comm. Math.
Phys., 265(3):673-697, 2006.
[8] Jeffrey H. ALBERT : Genericity of simple eigenvalues for
elliptic PDE's. Proc. Amer. Math. Soc., 48:413-418, 1975.
[9] Francesca ALBERTiNi et Domenico D'ALESSANDRo : Notions of
controllability for bilinear multilevel quantum systems. IEEE Trans.
Automat. Control, 48(8):1399-1403, 2003.
[10] François ALouGES, Antonio DESiMoNE et Aline LEFEBvRE
: Optimal strokes for low Reynolds number swimmers : an example. J.
Nonlinear Sci., 18(3):277-302, 2008.
[11] Claudio ALTAFiNi : Controllability properties for finite
dimensional quantum Markovian master equations. J. Math. Phys.,
44(6):23572372, 2003.
[12] B. D. O. ANDERSoN, R. R. BiTMEAD, C. R. JoHNSoN, P. V.
KoKoToviC, R. L. KoSuT, I. M. Y. MAREELS, L. PRALy et B. D. RiEDLE :
Stability of adaptive systems : Passivity and averaging analysis. MIT
Press, 1986.
[13] A. ASToLFi, D. CHHABRA et R. ORTEGA : Asymptotic
stabilization of some equilibria of an underactuated underwater vehicle.
Systems Control Lett., 45(3):193206, 2002.
[14] Moussa BALDE et Ugo BoSCAiN : Stability of planar switched
systems : the nondiagonalizable case. Commun. Pure Appl. Anal.,
7(1):121, 2008.
[15] John M. BALL, Jerrold E. MARSDEN et Marshall SLEMRoD :
Controllability for distributed bilinear systems. SIAM J. Control
Optim., 20(4):575597, 1982.
[16] Werner BALLMANN, Mikhael GRoMov et Viktor SCHRoEDER
: Manifolds of nonpositive curvature, volume 61 de Progress in
Mathematics. Birkhäuser Boston Inc., Boston, MA, 1985.
[17] David BAo, Shiing-Shen CHERN et Zhongmin SHEN : An
introduction to Riemann-Finsler geometry, volume 200 de Graduate Texts
in Mathematics. Springer-Verlag, New York, 2000.
[18] Nikita E. BARABANov : An absolute characteristic exponent
of a class of linear nonstationary systems of differential equations.
Sibirsk. Mat. Zh., 29(4):12-22, 222, 1988.
[19] Nikita E. BARABANov : Asymptotic behavior of extremal
solutions and structure of extremal norms of linear differential inclusions of
order three. Linear Algebra Appl., 428(10):2357-2367, 2008.
[20] B. Ross BARMiSH : Stabilization of uncertain systems via
linear control. IEEE Trans. Automat. Contr., 28(8):848-850, 1983.
[21] K. BEAuCHARD, Y. CHiTouR, D. KATES et R. LoNG : Spectral
controllability for 2D and 3D linear Schrödinger equations. J. Funct.
Anal., 256(12):3916-3976, 2009.
[22] Karine BEAuCHARD : Local controllability of a 1-D
Schrödinger equation. J. Math. Pures Appl. (9), 84(7):851-956,
2005.
[23] Karine BEAuCHARD : Control of Schrödinger
equations. Notes du Cours Peccot, Collège de France, 2007.
[24] Karine BEAuCHARD et Jean-Michel CoRoN : Controllability of
a quantum particle in a moving potential well. J. Funct. Anal.,
232(2):328-389, 2006.
[25] André BELLAICHE : The tangent space in
sub-Riemannian geometry. In Sub-Riemannian geometry, volume 144 de
Progr. Math., pages 1-78. Birkhäuser, Basel, 1996.
[26] H. C. BERG et R. ANDERSoN : Bacteria swim by rotating their
flagellar filaments. Nature, 245:380-382, 1973.
[27] J. BLAKE : A finite model for ciliated micro-organisms.
J. Biomech., 6:133-140, 1973.
[28] Franco BLANCHiNi et Stefano MiANi : Stabilization of LPV
systems : state feedback, state estimation, and duality. SIAM J. Control
Optim., 42(1):76-97, 2003.
[29] Anthony M. BLoCH, Roger W. BRoCKETT et Chitra RANGAN : The
controllability of infinite quantum systems and closed subspace criteria.
Preprint, 2006.
[30] Anthony M. BLoCH, Perinkulam Sambamurthy KRiSHNApRASAD,
Jerrold E. MARSDEN et Gloria Sánchez de ALvAREz : Stabilization of rigid
body dynamics by internal and external torques. Automatica J. IFAC,
28(4):745-756, 1992.
[31] Anthony M. BLoCH, Naomi Ehrich LEoNARD et Jerrold E.
MARSDEN : Stabilization of mechanical systems using controlled Lagrangians.
In Proceedings of the 36th IEEE Conference on Decision and Control, pages
2356-2361, 1997.
[32] Vincent D. BLoNDEL et Yurii NESTERov : Computationally
efficient approximations of the joint spectral radius. SIAM J. Matrix Anal.
Appl., 27(1):256272, 2005.
[33] Bernard BoNNARD, Jean-Baptiste CAiLLAu, Robert SiNCLAiR
et Minoru TANAKA : Conjugate and cut loci of a two-sphere of revolution with
application to optimal control. Ann. Inst. H. Poincaré Anal. Non
Linéaire, 26(4):10811098, 2009.
[34] Ugo BoSCAiN : Stability of planar switched systems : the
linear single input case. SIAM J. Control Optim., 41(1):89112,
2002.
[35] Ugo BoSCAiN, Thomas CHAMBRioN et Grégoire CHARLoT
: Nonisotropic 3-level quantum systems : complete solutions for minimum time
and minimum energy. Discrete Contin. Dyn. Syst. Ser. B, 5(4):957990,
2005.
[36] Ugo BoScAiN, Grégoire CHARLoT, Jean-Paul
GAuTHiER, Stéphane GuERiN et Hans-Rudolf JAuSLiN : Optimal control in
laser-induced population transfer for two- and three-level quantum systems.
J. Math. Phys., 43(5):2107-2132, 2002.
[37] Ugo BoScAiN et Benedetto PiccoLi : A short introduction to
optimal control. In T. SARi, éditeur : Contrôle Non
Linéaire et Applications, pages 19-66. Hermann, Paris, 2005.
[38] Stephen BoyD, Laurent EL GHAoui, Eric FERoN et
Venkataramanan BALAKRiSHNAN : Linear matrix inequalities in system and
control theory, volume 15 de SIAM Studies in Applied Mathematics.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA,
1994.
[39] C. BRENNEN : An oscil lating-boundary-layer theory for
ciliary propulsion. J. Fluid Mech., 65:799-824, 1974.
[40] Francesco BuLLo et Andrew D. LEwiS : Geometric
control of mechanical systems, volume 49 de Texts in Applied
Mathematics. Springer-Verlag, New York, 2005. Modeling, analysis, and
design for simple mechanical control systems.
[41] Mark S. ByRD et Navin KHANEjA : Characterization of the
positivity of the density matrix in terms of the coherence vector
representation. Phys. Rev. A (3), 68(6):062322, 13, 2003.
[42] Thomas CHAMBRioN : Approximate tracking for a system of
Schrödinger equations. Preprint, 2009.
[43] Stephen CHiLDRESS : Mechanics of swimming and
flying, volume 2 de Cambridge Studies in Mathematical Biology.
Cambridge University Press, Cambridge, 1981.
[44] Yacine CHiTouR : Applied and theoretical aspects of the
controllability of nonholonomic control system. PhD Thesis, Rutgers
University, 1996.
[45] Yacine CHiTouR, Jean-Michel CoRoN et Mauro GARAVELLo :
On conditions that prevent steady-state controllability of certain linear
partial differential equations. Discrete Contin. Dyn. Syst.,
14(4):643-672, 2006.
[46] Monique CHyBA, Naomi Ehrich LEoNARD et Eduardo D. SoNTAG
: Singular trajectories in multi-input time-optimal problems : application to
controlled mechanical systems. J. Dynam. Control Systems,
9(1):103-129, 2003.
[47] Monique CHyBA, Helmut MAuRER, Héctor J. SuSSMANN
et Vossen GoTTFRiED : Underwater vehicles : The minimum time problem. In
Proceedings of the 43th IEEE Conference on Decision and Control, pages
1370-1375, 2004.
[48] Yves Colin de VERDiERE : Sur une hypothèse de
transversalité d'Arnol'd. Comment. Math.
Helv., 63(2):184-193, 1988.
[49] Jean-Michel CoRoN : Control and nonlinearity,
volume 136 de Mathematical Surveys and Monographs. American
Mathematical Society, Providence, RI, 2007.
[50] Jamal DAAFouZ et Jacques BERNuSSou : Parameter dependent
Lyapunov functions for discrete time systems with time varying parametric
uncertainties. Systems Control Lett., 43(5):355359, 2001.
[51] René DAGER et Enrique ZuAZuA : Wave
propagation, observation and control in 1-d
flexible multi-structures, volume 50 de Mathématiques 6
Applications (Berlin) [Mathematics 6 Applications]. Springer-Verlag,
Berlin, 2006.
[52] Domenico D'ALESSANDRo : Introduction to quantum
control and dynamics. Applied Mathematics and Nonlinear Science Series.
Boca Raton, FL : Chapman, Hall/CRC., 2008.
[53] Wijesuriya P. DAyAwANsA et C. F. MARTiN : A converse
Lyapunov theorem for a class of dynamical systems which undergo switching.
IEEE Trans. Automat. Control, 44(4):751- 760, 1999.
[54] Lester E. DuBiNs : On curves of minimal length with a
constraint on average curvature, and with prescribed initial and terminal
positions and tangents. Amer. J. Math., 79:497- 516, 1957.
[55] Sylvain ERVEDozA et Jean-Pierre PuEL : Approximate
controllability for a system of Schrödinger equations modeling a single
trapped ion. Ann. Inst. H. Poincaré Anal. Non Linéaire,
26:2111-2136, 2009.
[56] Eric FERoN, Pierre APKARiAN et Pascal GAHiNET : Analysis
and synthesis of robust control systems via parameter-dependent Lyapunov
functions. IEEE Trans. Automat. Control, 41(7):1041-1046, 1996.
[57] Bruno FRANCHi et Ermanno LANCoNELLi : Une
métrique associée à une classe d'opérateurs
elliptiques dégénérés. Rend. Sem. Mat. Univ.
Politec. Torino, (Special Issue):105-114 (1984), 1983. Conference on
linear partial and pseudodifferential operators (Torino, 1982).
[58] D. FRENKEL et R. PoRTuGAL : Algebraic methods to compute
Mathieu functions. J. Phys. A, 34(17):3541-3551, 2001.
[59] Giovanni P. GALDi : An introduction to the
mathematical theory of the Navier-Stokes equations. Vol. I, volume 38
de Springer Tracts in Natural Philosophy. Springer-Verlag, New York,
1994. Linearized steady problems.
[60] Jean-Paul GAuTHiER et Ivan A. K. KuPKA : Observability and
observers for nonlinear systems. SIAM J. Control Optim.,
32(4):975-994, 1994.
[61] José C. GERoMEL et Patrizio CoLANERi : Robust
stability of time varying polytopic systems. Systems Control Lett.,
55(1):81-85, 2006.
[62] V. V. GRuS'iN : A certain class of hypoelliptic
operators. Mat. Sb. (N.S.), 83 (125):456-473, 1970.
[63] Alain HARAuX, Patrick MARTiNEz et Judith VANCosTENoBLE :
Asymptotic stability for intermittently controlled second-order evolution
equations. SIAM J. Control Optim., 43(6):2089-2108, 2005.
[64] Pascal HEBRARD et Antoine HENRoT : Optimal shape and
position of the actuators for the stabilization of a string. Systems
Control Lett., 48(3-4):199-209, 2003. Optimization and control of
distributed systems.
[65] Dan HENRy : Perturbation of the boundary in
boundary-value problems of partial differential equations, volume 318
de London Mathematical Society Lecture Note Series. Cambridge
University Press, Cambridge, 2005. With editorial assistance from Jack Hale and
Antônio Luiz Pereira.
[66] Luc HiLLAiRET et Chris JuDGE : Generic spectral simplicity
of polygons. Proc. Amer. Math. Soc., 137(6):21392145, 2009.
[67] Patrick HCHLER, Joachim BARGoN et Steffen J GLAsER :
Nuclear magnetic resonance quantum computing exploiting the pure spin state of
para hydrogen. J. Chem. Phys., 113(6):20562059, 2000.
[68] Velimir JuRDjEViC : Geometric control theory,
volume 52 de Cambridge Studies in Advanced Mathematics. Cambridge
University Press, Cambridge, 1997.
[69] Tosio KATo : Perturbation theory for linear
operators. Die Grundlehren der mathematischen Wissenschaften, Band 132.
Springer-Verlag New York, Inc., New York, 1966.
[70] Horace LAMB : Hydrodynamics. Cambridge
Mathematical Library. Cambridge University Press, Cambridge, sixth
édition, 1993. With a foreword by R. A. Caflisch [Russel E.
Caflisch].
[71] Pier Domenico LAMBERTi et Massimo LANZA DE CRisToFoRis :
Persistence of eigenvalues and multiplicity in the Dirichlet problem for the
Laplace operator on nonsmooth domains. Math. Phys. Anal. Geom.,
9(1):65-94, 2006.
[72] Naomi Ehrich LEoNARD : Mechanics and nonlinear control :
Making underwater vehicles ride and glide. In Proc. 4th IFAC Nonlinear
Control Design Symp., pages 1-6, 1998.
[73] Daniel LiBERZoN : Switching in systems and
control. Systems & Control : Foundations & Applications.
Birkhäuser Boston Inc., Boston, MA, 2003.
[74] James LiGHTHiLL : Mathematical
biofluiddynamics. Society for Industrial and Applied Mathematics,
Philadelphia, Pa., 1975. Based on the lecture course delivered to the
Mathematical Biofluiddynamics Research Conference of the National Science
Foundation held from July 16-20, 1973, at Rensselaer Polytechnic Institute,
Troy, New York, Regional Conference Series in Applied Mathematics, No. 17.
[75] Jacques-Louis LioNs et Enrique ZuAZuA : A generic
uniqueness result for the Stokes system and its control theoretical
consequences. In Partial differential equations and applications,
volume 177 de Lecture Notes in Pure and Appl. Math., pages 221-235.
Dekker, New York, 1996.
[76] Daniela Lupo et Anna Maria MiCHELETTi : A remark on the
structure of the set of perturbations which keep fixed the multiplicity of two
eigenvalues. Rev. Mat. Apl., 16(2): 47-56, 1995.
[77] Michael MARGALioT et Christos YFouLis : Absolute stability
of third-order systems : a numerical algorithm. Automatica J. IFAC,
42(10):1705-1711, 2006.
[78] Paolo MAsoN, Ugo BosCAiN et Yacine CHiTouR : Common
polynomial Lyapunov functions for linear switched systems. SIAM journal on
control and optimization, 45:226-245, 2006.
[79] T.A. MEYNARD, H. FoCH, P. THoMAs, J. CouRAuLT, R. JAkoB
et M. NAHRsTAEDT : Multicell converters : basic concepts and industry
applications. IEEE Transactions on Industrial Electronics,
49(5):955-964, 2002.
[80] Anna Maria MiCHELETTi : Perturbazione dello spettro
dell'operatore di Laplace, in relazione ad una variazione del campo. Ann.
Scuola Norm. Sup. Pisa (3), 26:151-169, 1972.
[81] Mazyar MiRRAHiMi : Lyapunov control of a particle in a
finite quantum potential well. In Proceedings of the 45th IEEE Conference
on Decision and Control, 2006.
[82] Mazyar MiRRAHiMi : Lyapunov control of a quantum particle
in a decaying potential. Ann. Inst. H. Poincaré Anal. Non
Linéaire, 26(5):1743-1765, 2009.
[83] Mazyar MiRRAHiMi et Pierre RouCHoN : Controllability of
quantum harmonic oscillators. IEEE Trans. Automat. Control,
49(5):745747, 2004.
[84] Dirk MiTTENHuBER : Dubins' problem in the hyperbolic
plane using the open disc model. In Geometric control and non-holonomic
mechanics (Mexico City, 1996), volume 25 de CMS Conf. Proc.,
pages 115152. Amer. Math. Soc., Providence, RI, 1998.
[85] Dirk MiTTENHuBER : Dubins' problem is intrinsically
three-dimensional. ESAIM Control Optim. Calc. Var., 3:122, 1998.
[86] Felipe MoNRoY-PEREZ : Three-dimensional non-Euclidean
Dubins' problem. In Geometric control and non-holonomic mechanics (Mexico
City, 1996), volume 25 de CMS Conf. Proc., pages 153181. Amer.
Math. Soc., Providence, RI, 1998.
[87] Vahagn NERsEsyAn : Growth of Sobolev norms and
controllability of the Schrödinger equation. Comm. Math. Phys.,
290(1):371-387, 2009.
[88] S. P. Novikov et I.
ShmEL'tsER : Periodic solutions of Kirchhoff
equations for the free motion of a rigid body in a fluid and the extended
Lyusternik-Shnirel'man-Morse theory. I.
Funktsional. Anal. i Prilozhen., 15(3):54-66, 1981.
[89] Jaime H. ORtEgA et Enrique ZuAzuA : Generic simplicity of
the spectrum and stabilization for a plate equation. SIAM J. Control
Optim., 39(5):1585-1614, 2000.
[90] Jaime H. ORtEgA et Enrique ZuAzuA : Generic simplicity of
the eigenvalues of the Stokes system in two space dimensions. Adv.
Differential Equations, 6(8):987-1023, 2001.
[91] A PEiRcE, M DAhLEh et H RAbitz : Optimal control of quantum
mechanical systems: Existence, numerical approximations, and applications.
Phys. Rev. A, 37:4950-4964, 1988.
[92] Fernand PELLEtiER : Sur le théorème de
Gauss-Bonnet pour les pseudo-métriques singulières. In
Séminaire de Théorie Spectrale et Géométrie, No. 5,
Année 1986-1987, pages 99-105. Univ. Grenoble I, Saint, 1987.
[93] V. Yu. PRotAsov : A generalized joint spectral radius. A
geometric approach. Izv. Ross. Akad. Nauk Ser. Mat., 61(5):99-136,
1997.
[94] E. M. PuRcELL : Life at low Raynolds numbers. Am. J.
Phys., 45:3-11, 1977.
[95] H. RAbitz, H. de ViviE-RiEdLE, R. Motzkus et K. KompA :
Wither the future of controlling quantum phenomena? SCIENCE,
288:824-828, 2000.
[96] Rajamani RAvi, Krishan M. NAgpAL et Pramod P.
KhARgonEkAR : H8 control of linear time-varying
systems : a state-space approach. SIAM J. Control Optim.,
29(6):1394-1413, 1991.
[97] Michael REEd et Barry Simon : Methods of modern
mathematical physics. IV. Analysis of operators. Academic Press [Harcourt
Brace Jovanovich Publishers], New York, 1978.
[98] Franz RELLich : Perturbation theory of eigenvalue
problems. Assisted by J. Berkowitz. With a preface by Jacob T. Schwartz.
Gordon and Breach Science Publishers, New York, 1969.
[99] Sérgio S. RodRiguEs : Navier-Stokes equation on the
rectangle controllability by means of low mode forcing. J. Dyn. Control
Syst., 12(4):517-562, 2006.
[100] Pierre Rouchon : Control of a quantum particle in a
moving potential well. In Lagrangian and Hamiltonian methods for nonlinear
control 2003, pages 287-290. IFAC, Laxenburg, 2003.
[101] Jorge SAn MARtín, Takéo TAkAhAshi et Marius
TucsnAk : A control theoretic approach to the swimming of microscopic
organisms. Quart. Appl. Math., 65:405-424, 2007.
[102] T. SEidEmAn et E. HAmiLton : Nonadiabatic alignment by
intense pulses : concepts, theory and directions. Adv. At. Mol. Opt.
Phys., 52:289, 2006.
[103] M. ShApiRo et P. BRumER : Principles of the Quantum
Control of Molecular Processes. Principles of the Quantum Control of
Molecular Processes, pp. 250. Wiley-VCH, février 2003.
[104] Takashi ShioyA : The limit spaces of two-dimensional
manifolds with uniformly bounded integral curvature. Trans. Amer. Math.
Soc., 351(5):17651801, 1999.
[105] M. SpAnnER, E. A. ShApiRo et M. IvAnov : Coherent control
of rotational wave-packet dynamics via fractional revivals. Phys. Rev.
Lett., 92:093001, 2004.
[106] Michael SpivAk : A comprehensive introduction to
differential geometry. Vol. II. Publish or Perish Inc., Wilmington, Del.,
second édition, 1979.
[107] H. STApELFELDT et T. SEiDEMAN : Aligning molecules with
strong laser pulses. Rev. Mod. Phys., 75:543, 2003.
[108] D. SUGNy, A. KELLER, O. ATABEK, D. DAEMS, C. DioN, S.
GUERiN et H. R. JAUSLiN : Reaching optimally oriented molecular states by laser
kicks. Phys. Rev. A, 69:033402, 2004.
[109] H. J. SUSSMANN et G. TANG : Shortest paths for the
Reeds-Shepp car : a worked out example of the use of geometric techniques in
nonlinear optimal control. Rutgers Center for Systems and Control Technical
Report 91-10, 1991.
[110] Héctor J. SUSSMANN : Shortest 3-dimensional paths
with a prescribed curvature bound. In Proceedings of the 34th IEEE
Conference on Decision and Control, 1995.
[111] G. TAyLoR : Analysis of the swimming of microscopic
organisms. Proc. Roy. Soc. London. Ser. A., 209:447-461, 1951.
[112] Stefan TEUFEL : Adiabatic perturbation theory in
quantum dynamics, volume 1821 de Lecture Notes in Mathematics.
Springer-Verlag, Berlin, 2003.
[113] Mikhail TEyTEL : How rare are multiple eigenvalues?
Comm. Pure Appl. Math., 52(8): 917-934, 1999.
[114] Gabriel TURiNici : On the controllability of bilinear
quantum systems. In M. DEFRANcEScHi et C. LE BRiS, éditeurs
: Mathematical models and methods for ab initio Quantum Chemistry,
volume 74 de Lecture Notes in Chemistry. Springer, 2000.
[115] Karen UHLENBEcK : Eigenfunctions of Laplace operators.
Bull. Amer. Math. Soc., 78: 1073-1076, 1972.
[116] Enrique ZUAzUA : Switching controls. Journal of the
European Mathematical Society, à paraître.