Flatness and defect of non-linear systems: introductory theory and examples

ACHESON , D. , 1993 , A pendulum theorem .Proceedings of the Royal Society of London, Series A, 443 , 239 – 245 .

BAILLIEUL J., 1993, Dynamics and Control of Mechanical Systems, 1

10.1109/TAC.1987.1104698

10.1007/978-1-4612-4438-7

10.1137/0331057

BUSHNELL , L. TILBURY , D. , and SASTRY , S. , 1993 , Steering chained form nonholonomic systems using sinusoids the firetruck example .Proceedings of the European Control Conference (ECC'93), Groningen , pp. 1432 – 1437 .

CAMPION G., 1992, Lecture Notes of the Summer School on Theory of Robots

10.1515/crll.1915.145.86

10.1016/0167-6911(89)90031-5

CLAUDE D., 1986, Algebraic and Geometric Methods in Nonlinear Control Theory, 181, 10.1007/978-94-009-4706-1_11

COHN P. M., 1985, Free Rings and Their Relations

10.1007/BF01211563

CORON J. M., 1992, Proceedings of the IFAC Symposium on Nonlinear Control Systems Design, 658

D'ANDRÉA-NOVEL B., 1990, Robust Control of Linear and Nonlinear Systems, Mathematical Theory of Networks and Systems (MTNS'89), 523, 10.1007/978-1-4612-4484-4_52

10.1109/ROBOT.1992.220061

D'ANDRÉA-NOVEL B., 1992, Recent Advances in Mathematical Theory of Systems, Control, NetworkSignal Processing II, Mathematical Theory of NetworksSystems (MTNS’89), 321

DELALEAU E., 1992, Comptes Rendus Hebdomadaires des Seances de I’Academie des Sciences, Serie I, 315, 101

10.1137/0327035

10.1007/BF02551378

DUBROVIN B., 1984, Modern Geometry—Methods and Applications—Part 1, 10.1007/978-1-4684-9946-9

10.1515/form.1989.1.227

FLIESS M., 1993, Essays on Control Perspectives in the Theory and its Applications, 223, 10.1007/978-1-4612-0313-1_8

FLIESS M., 1990, Realization and Modelling in System Theory, MTNS’89, 1

FLIESS , M. LÉVINE , J. , and ROUCHON , P. , 1991 , A simplified approach of crane control via a generalized state-space model .Proceedings of the 30th IEEE Conference on Decision and Control, Brighton , U.K. , pp. 736 – 741 ; 1993 a, A generalized state variable representation for a simplified crane description.International Journal of Control,58, 277–283 .

FLIESS M., 1992, Proceedings of the IFAC Symposium on Nonlinear Control Systems Design (NOLCOS’92), 408

10.1007/978-1-4612-1140-2

10.1007/978-1-4757-3849-0

10.1007/BF01456663

10.1007/978-3-662-02581-9

JACOBSON N., 1985, Basic Algebra, I and II

JAKUBCZYK , B. , 1992 , Remarks on equivalence and linearization of nonlinear systems .Proceedings of the IFAC Symposium on Nonlinear Control Systems Design (NOLCOS'92), Bordeaux , France , pp. 393 – 397 .

10.2307/1970810

KAILATH T., 1980, Linear Systems

KOLCHIN E., 1973, Differential Algebra and Algebraic Groups

LANDAU L., 1982, Mechanics

LAUMOND J., 1991, IEEE International Conference on Advanced Robotics, 91 ICAR, 1033

10.1109/70.326564

10.1080/00207178708933798

MARTIN , P. , 1992 , Contribution à létude des systémes diffèrentiellement plats . Ph.D. thesis , École des Mines de Paris ; 1993, An intrinsic condition for regular decoupling. Systems Control Letters, 20, 383–391 .

MARTIN , P. , and ROUCHON , P. , 1993 , Systems without drift and flatness .Proceedings of the Conference on Mathematical Theory of Networks and Systems (MTNS'93), Regensburg , Germany .

10.1109/13.57076

10.1109/TAC.1980.1102426

MONACO , S. , and NORMAND-CYROT , D. , 1992 , An introduction to motion planning under multirate digital control .Proceedings of the 31st IEEE Conference on Decision and Control, Tucson , Arizona , U.S.A. , pp. 7180 – 1785 .

MOOG , C. PERRAUD , J. BENTZ , P. , and Vo , Q. T. , 1989 , Prime differential ideals in nonlinear rational control systems .Proceedings of the Symposium on Nonlinear Control Systems Design (NOLCOS'89), Capri , Italy , pp. 178 – 182 .

10.1109/9.277235

10.1007/978-1-4757-2101-0

POMET J., 1993, Workshop on Geometry in Nonlinear Control

RITT J., 1950, Differential Algebra, 10.1090/coll/033

ROUCHON P., 1994, Journal of Mathematical Systems, Estimation and Control, 4, 257

ROUCHON P., 1993, Proceedings of the European Control Conference (ECC'93), 1518

SAGDEEV R., 1988, Nonlinear Physics

SEIDENBERG A., 1952, Transactions of the American Mathematical Society, 73, 174

10.1016/0167-6911(90)90041-R

10.1080/00207178808906030

10.1080/14786440809463763

10.1016/0022-0396(72)90007-1

SUSSMANN , H. J. , and Liu , W. , 1991 , Limits of high oscillatory controls and the approximation of general paths by admissible trajectories . Proceedings of the 30th IEEE Conference on Decision and Control , Brighton , U.K. , pp. 437 – 442 .

TCHOŃ K., 1994, Journal of Mathematical Systems, Estimation and Control, 4, 165

TIKHONOV A., 1980, Differential Equations

TILBURY , D. , and CHELOUAH , A. , 1993 , Steering a three-input nonholonomic using multirate controls .Proceedings of the European Control Conference (ECC93), Groningen , The Netherlands , pp. 1428 – 1431 .

TILBURY , D. SORDALEN , O. BUSHNELL , L. , and SASTRY , S. , 1993 , A multi-steering trailer system conversion into chained form using dynamic feedback . Technical Report UCB/ERL M93/55 . Electronics Research Laboratory, University of California at Berkeley .

WHITTAKER E., 1937, A Treatise on the Analytical Dynamics of Particules and Rigid Bodies

10.1109/9.73561

10.1007/978-1-4757-6802-2