H. Ahn, Y. Chen, and H. Dou, State-periodic adaptive compensation of cogging and coulomb friction in permanent-magnet linear motors, IEEE Transactions on Magnetics, vol.41, issue.1, 2005.

S. Balemi, AUTOMATIC CALIBRATION OF SINUSOIDAL ENCODER SIGNALS, Proceedings of the 16th IFAC World Congress, 2005.
DOI : 10.3182/20050703-6-CZ-1902.01190

M. Carl, S. A. Bender, and . Orszag, Advanced Mathematical Methods for Scientists and Engineers I, Asymptotic Methods and Perturbation Theory, 1999.

J. Steven, Y. Benson, and . Ye, DSDP5: Software for semidefinite programming, 2005.

J. Steven, Y. Benson, and . Ye, DSDP5 user guide ? software for semidefinite programming, 2005.

J. Boichot, E. Delaleau, N. V. Diep, J. Lévine, and E. Parzy, Modeling and control of a high-precision positioning system actuated by a linear synchronous motor, Proceedings of the IFAC World Congress, 1999.

J. Boichot, E. Delaleau, N. V. Diep, J. Lévine, and E. Parzy, Modeling and control of a two D.O.F. high-precision positioning system, Proceedings of the European Conference on Control, 1999.

B. Borchers, A c library for semidefinite programming. Optimization Methods and Software, pp.597-611, 1999.

B. Borchers, Csdp 2.3 user's guide. Optimization Methods and Software, pp.597-611, 1999.

R. W. Brockett, Finite Dimensional Linear Systems, 1970.
DOI : 10.1137/1.9781611973884

B. H. Bukkems, D. Kostic, A. G. De-jager, and S. Maarten, Learning-based identification and iterative learning control of direct-drive robots, IEEE Transactions on Control Systems Technology, vol.13, issue.4, 2005.
DOI : 10.1109/TCST.2005.847335

C. Canudas, D. Wit, and L. Praly, Adaptive eccentricity compensation, IEEE Transactions on Control Systems Technology, vol.8, issue.5, 2000.

A. Earl, N. Coddington, and . Levinson, Theory of Ordinary Differential Equations, 1955.

L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansion, 1974.
DOI : 10.1007/978-94-010-2196-8

J. C. Culioli, IntroductionàIntroduction`Introductionà l'Optimisation. Ellipses, 1994.

R. Dhaouadi, N. Mohan, and L. Norum, Design and implementation of an extended Kalman filter for the state estimation of a permanent magnet synchronous motor, IEEE Transactions on Power Electronics, vol.6, issue.3, pp.491-497, 1991.
DOI : 10.1109/63.85891

J. Dieudonné, ´ Eléments d'Analyse, volume 1. Fondements de l'Analyse Moderne, 1969.

F. Faa-d-`-i and . Bruno, Note sur une nouvelle formule de calcul différentiel, Quarterly Journal of Pure and Applied Mathematics, vol.1, pp.359-360, 1857.

A. F. Filippov, Differential Equations with Discontinuous Righthand Sides, 1988.
DOI : 10.1007/978-94-015-7793-9

J. Guckenheimer and P. Holmes, Nonlinear oscillations, Dynamical Systems and Bifurcations of Vector Fields, 1986.

P. L. Heydemann, Determination and correction of quadrature fringe measurement errors in interferometers, Applied Optics, vol.20, issue.19, pp.3382-3384, 1981.
DOI : 10.1364/AO.20.003382

M. S. Islam, S. Mir, and T. Sebastian, Issues in reducing the cogging torque of mass-produced permanent-magnet brushless dc motor, IEEE Transactions on Industry Applications, vol.40, issue.3, 2004.

P. Warren and . Jonhson, The curious history of faa d` ? bruno formula, American Mathematical Monthly, vol.109, pp.217-234, 2002.

A. B. Kulkarni and M. Ehsani, A noval position sensor elimination technique for the interior permanent magnet synchronous motor drive, IEEE, Transactions on Industry Applications, pp.144-150, 1992.

J. Löfberg, YALMIP : a toolbox for modeling and optimization in MATLAB, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), 2004.
DOI : 10.1109/CACSD.2004.1393890

K. W. Lim, K. S. Low, and M. F. Rahman, Observers for sensorless control of permanent magnet synchronous motor drive, Proceedings of the IFAC World Congress, pp.431-434, 1993.

J. Lévine and . Van-diep-nguyen, Flat output characterization for linear systems using polynomial matrices, Systems & Control Letters, vol.48, issue.1, pp.69-75, 2003.
DOI : 10.1016/S0167-6911(02)00257-8

J. Malaizé, Devices and methods for cogging force cancellation in linear motors, 2007.

J. Malaizé, R. Desailly, J. Lévine, F. Duquenoy, and D. Gvero, Apparatus and method for estimation of initial phase of a brushless motor, 2006.

J. Malaizé and J. Lévine, Active estimation of the initial phase for brushless synchronous motors, 9th IEEE International Workshop on Advanced Motion Control, 2006., 2006.
DOI : 10.1109/AMC.2006.1631721

J. Malaizé and J. Lévine, Estimation active de la phase initiale des moteurs synchrones, Actes de la Conférence Internationale Française d'Automatique, 2006.

R. J. Merry, M. J. Van-de-molengraft, and M. Steinbuch, Iterative learning control with wavelet filtering, International Journal of Robust and Nonlinear Control, vol.109, issue.10, 2007.
DOI : 10.1002/rnc.1239

T. Noguchi, K. Yamada, S. Kondo, and I. Takahashi, Initial rotor position estimation method of sensorless PM synchronous motor with no sensitivity to armature resistance, IEEE Transactions on Industrial Electronics, vol.45, issue.1, pp.118-125, 1998.
DOI : 10.1109/41.661312

S. Ogasawara and H. Agaki, An approach to real time position estimation at zero and low speed for a PM motor based on saliency, IEEE, Proceedings of the Industry Applications Society Annual Meeting, pp.29-35, 1996.

S. Ostlund and M. Brokemper, Sensorless rotor-position detection from zero to rated speed for an integrated PM synchronous motor drive, IEEE Transactions on Industry Applications, vol.32, issue.5, pp.1158-1165, 1996.
DOI : 10.1109/28.536878

G. Otten, J. A. Theo-de-vries, J. Van-amerongen, M. A. Rankers, and W. E. Gall, Linear motor motion control using a learning feedforward controller, IEEE/ASME Transactions on Mechatronics, vol.2, issue.3, 1997.
DOI : 10.1109/3516.622970

P. B. Schmidt, M. L. Gasperi, G. Ray, and A. H. Wijenayake, Initial rotor angle detection of a nonsalient pole permanent magnet synchronous machine, IAS '97. Conference Record of the 1997 IEEE Industry Applications Conference Thirty-Second IAS Annual Meeting, pp.459-463, 1997.
DOI : 10.1109/IAS.1997.643063

L. M. Silverman, Transformation of time-variable systems to canonical (phase-variable) form, IEEE Transactions on Automatic Control, vol.11, issue.2, 1966.
DOI : 10.1109/TAC.1966.1098312

L. M. Silverman and H. E. Meadows, Controllability and Observability in Time-Variable Linear Systems, SIAM Journal on Control, vol.5, issue.1, 1967.
DOI : 10.1137/0305005

N. Singer, W. Singhose, and W. Seering, Comparison of Filtering Methods for Reducing Residual Vibration, European Journal of Control, vol.5, issue.2-4, pp.208-218, 1999.
DOI : 10.1016/S0947-3580(99)70155-X

F. Jos and . Sturm, Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones. Optimization Methods and Software, pp.625-653, 1999.

K. K. Tan, S. N. Huang, and T. H. Lee, Robust adaptive numerical compensation for friction anf force ripple in permanent-magnet linear motor, IEEE Transactions on Magnetics, vol.38, issue.1, 2002.

T. Kok-kiong and K. Tang, Adaptive online correction and interpolation of quadrature encoder signals using radial basis functions, IEEE Transactions on Control Systems Technology, vol.13, issue.3, pp.370-377, 2005.
DOI : 10.1109/TCST.2004.841648

E. Temple-bell51, ]. K. Van-berkel, I. Rotariu, and M. Steinbuch, Partition polynomials Cogging compensating piecewise iterative learning control for variable setpoints with application to a wafer stage, Proceedings of the 26th American Control Conference, pp.38-46, 1927.

M. Van-dyke, Perturbation Method in Fluid Mechanics, Journal of Applied Mechanics, vol.43, issue.1, 1964.
DOI : 10.1115/1.3423785

J. Wang, D. Howe, and G. W. , Fringing in tubular permanent-magnet machines: Part I, magnetic field distribution, flux linkage, and thrust force, IEEE Transactions on Magnetics, vol.39, issue.6, 2003.

J. Wang, D. Howe, and . Geraintw, Fringing in tubular permanent-magnet machines: Part II, cogging force and its minimization, IEEE Transactions on Magnetics, vol.39, issue.6, 2003.

X. Wang, Y. Yang, and D. Fu, Study of cogging torque in surface-mounted permanent magnet motors with energy method, Journal of Magnetism and Magnetic Materials, vol.267, issue.1, 2003.
DOI : 10.1016/S0304-8853(03)00324-X

A. William and . Wolovich, On the stabilization of controllable systems, IEEE Transaction on Automatic Control, 1968.

. ?i, 1 ? i ? n ? r + 1, 0 ? x i ? y i =? B n,r (x 1 , . . . , x n?r+1 ) ? B n,r (y 1