Free access
Issue
ESAIM: COCV
Volume 4, 1999
Page(s) 1 - 35
DOI http://dx.doi.org/10.1051/cocv:1999101
Published online 15 August 2002
  1. M.K. Bennani and P. Rouchon, Robust stabilization of flat and chained systems, in European Control Conference (ECC) (1995) 2642-2646.
  2. R.W. Brockett, Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, R.S. Millman R.W. Brockett and H.H. Sussmann Eds., Birkauser (1983).
  3. C. Canudas de Wit and O. J. Sørdalen, Exponential stabilization of mobile robots with nonholonomic constraints. IEEE Trans. Automat. Control 37 (1992) 1791-1797. [CrossRef] [MathSciNet]
  4. M. Fliess, J. Lévine, P. Martin and P. Rouchon, Flatness and defect of non-linear systems: introductory theory and examples. Internat. J. Control 61 (1995) 1327-1361. [CrossRef] [MathSciNet]
  5. H. Hermes, Nilpotent and high-order approximations of vector field systems. SIAM Rev. 33 (1991) 238-264. [CrossRef] [MathSciNet]
  6. A. Isidori, Nonlinear control systems. Springer Verlag, third edition (1995).
  7. M. Kawski, Geometric homogeneity and stabilization, in IFAC Nonlinear Control Systems Design Symp. (NOLCOS) (1995) 164-169.
  8. I. Kolmanovsky and N.H. McClamroch, Developments in nonholonomic control problems. IEEE Control Systems (1995) 20-36.
  9. J. Kurzweil and J. Jarnik, Iterated lie brackets in limit processes in ordinary differential equations. Results in Mathematics 14 (1988) 125-137.
  10. Z. Li and J.F. Canny, Nonholonomic motion planning. Kluwer Academic Press (1993).
  11. W. Liu, An approximation algorithm for nonholonomic systems. SIAM J. Contr. Opt. 35 (1997) 1328-1365. [CrossRef] [MathSciNet]
  12. D.A. Lizárraga, P. Morin and C. Samson, Non-robustness of continuous homogeneous stabilizers for affine systems. Technical Report 3508, INRIA (1998). Available at http://www.inria.fr/RRRT/RR-3508.html
  13. R.T. M'Closkey and R.M. Murray, Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE Trans. Automat. Contr. 42 (1997) 614-628. [CrossRef] [MathSciNet]
  14. S. Monaco and D. Normand-Cyrot, An introduction to motion planning using multirate digital control, in IEEE Conf. on Decision and Control (CDC) (1991) 1780-1785.
  15. P. Morin, J.-B. Pomet and C. Samson, Design of homogeneous time-varying stabilizing control laws for driftless controllable systems via oscillatory approximation of lie brackets in closed-loop. SIAM J. Contr. Opt. (to appear).
  16. P. Morin, J.-B. Pomet and C. Samson, Developments in time-varying feedback stabilization of nonlinear systems, in IFAC Nonlinear Control Systems Design Symp. (NOLCOS) (1998) 587-594.
  17. P. Morin and C. Samson, Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics. Technical Report 3477, INRIA (1998).
  18. R.M. Murray and S.S. Sastry, Nonholonomic motion planning: Steering using sinusoids. IEEE Trans. Automat. Contr. 38 (1993) 700-716. [CrossRef] [MathSciNet]
  19. L. Rosier, Étude de quelques problèmes de stabilisation. PhD thesis, École Normale de Cachan (1993).
  20. C. Samson, Velocity and torque feedback control of a nonholonomic cart, in Int. Workshop in Adaptative and Nonlinear Control: Issues in Robotics. LNCIS, Vol. 162, Springer Verlag, 1991 (1990).
  21. O.J. Sørdalen and O. Egeland, Exponential stabilization of nonholonomic chained systems. IEEE Trans. Automat. Contr. 40 (1995) 35-49. [CrossRef] [MathSciNet]
  22. G. Stefani, Polynomial approximations to control systems and local controllability, in IEEE Conf. on Decision and Control (CDC) (1985) 33-38.
  23. G. Stefani, On the local controllability of scalar-input control systems, in Theory and Applications of Nonlinear Control Systems, Proc. of MTNS'84, C.I. Byrnes and A. Linsquist Eds., North-Holland (1986) 167-179.
  24. H.J. Sussmann and W. Liu, Limits of highly oscillatory controls ans approximation of general paths by admissible trajectories, in IEEE Conf. on Decision and Control (CDC) (1991) 437-442.
  25. H.J. Sussmann, Lie brackets and local controllability: a sufficient condition for scalar-input systems. SIAM J. Contr. Opt. 21 (1983) 686-713. [CrossRef]
  26. H.J. Sussmann, A general theorem on local controllability. SIAM J. Contr. Opt. 25 (1987) 158-194. [CrossRef] [MathSciNet]