Necessary and Sufficient Condition for Global Controllability of a Class of Affine Nonlinear Systems

1. A. Isidori, Nonlinear Control Systems, third ed. Springer-Verlag, London, 1995.

   Google Scholar 

2. J. L. Casti, Nonlinear System Theory, Academic Press, Inc. Ltd., Orlando, 1985.

   Google Scholar 

3. H. Nijmeijer and A. van der Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag, New York, 1990.

   Google Scholar 

4. E. D. Sontag, Mathematical Control Theory—Deterministic Finite Dimensional Systems, Springer-Verlag, New York, 1998.

   Google Scholar 

5. V. Jurdjevic, Geometric Control Theory, Cambridge University Press, New York, 1997.

   Google Scholar 

6. G. W. Haynes and H. Hermes, Nonlinear controllability via lie theory, SIAM J. Control, 1970, 8(4): 450–460.

   Article  Google Scholar 

7. H. J. Sussmann and V. Jurdjevic, Controllability of nonlinear systems, J. Diff. Eqns. 1972, 12(1): 95–116.

   Article  Google Scholar 

8. Y. M. Sun, Necessary and sufficient condition for global controllability of planar affine nonlinear systems, IEEE Trans. Automat. Contr., 2007, 52(8): 1454–1460.

   Article  Google Scholar 

9. Y. M. Sun and L. Guo, On global controllability of planar affine nonlinear systems, Proceedings of the 24th Chinese Control Conference, South China University of Technology Press, 2005, 1765–1769.

10. L. R. Hunt, Global controllability of nonlinear systems in two dimensions, Math. Systems Theory, 1980, 13: 361–376.

    Article  Google Scholar 

11. D. Aeyels, Local and global controllability for nonlinear systems, Systems & Control Letters, 1984, 5(1): 19–26.

    Article  Google Scholar 

12. C. Y. Kaya and J. L. Noakes, Closed trajectories and global controllability in the plane, IMA Journal of Mathematical Control & Information, 1997, 14(4): 353–369.

    Article  Google Scholar 

13. P. E. Caines and E. S. Lemch, On the global controllability of nonlinear systems: fountains, recurrence, and applications to hamiltonian systems, SIAM J. Cotrol Optim., 2003, 41(5): 1532–1553.

    Article  Google Scholar 

14. L. R. Hunt, n-Dimensional controllability with (n − 1) controls, IEEE Trans. Automat. Contr., 1982, 27(1): 113–117.

    Article  Google Scholar 

15. S. Nikitin, Global Controllability and Stabilization of Nonlinear Systems,World Scientific Publishing Co. Pte. Ltd, Singapore, 1994.

    Google Scholar 

16. D. Cheng, Controllability of Switched Affine Systems, Proceedings of the 24th Chinese Control Conference, South China University of Technology Press, 2005, 1770–1775.

17. Y. M. Sun, S. W. Mei, and Q. Lu, On Global Controllability of Affine Nonlinear Systems with a Triangular-like Structure, Science in China (Series. F, Information Science), 2007, 50(6): 831–845.

    Google Scholar 

18. F. Bullo and A. D. Lewis, Geometric Control of Mechanical Systems, Modeling, Analysis, and Design for Simple Mechenical Control Systems (Texts In Applied Methematics), Springer, New York, 2005.

    Google Scholar 

19. Y. Guo, Z. Xi, and D. Cheng, Speed rugulation of permanent magnet synchrorous motor via feedback dissipative hamiltonian realization, Control Theory & Applications, IET, 2007, 1(1): 281–290.

    Article  Google Scholar 

20. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley & Sons, Inc, New York, 1995.

    Google Scholar 

21. P. Hartman, Ordinary Differential Equations, Second ed. Birkhäuser, Boston, 1982, 25–27.

    Google Scholar 

22. H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc., 1934, 34(1): 63–89.

    Article  Google Scholar 

23. V. I. Arnold, Ordinary Differential Equations (Translated and edited by R. A. Silverman), MIT Press, Cambridge, 1973.

Download references