Free access
Issue
ESAIM: COCV
Volume 4, 1999
Page(s) 537 - 557
DOI http://dx.doi.org/10.1051/cocv:1999121
Published online 15 August 2002
  1. F. Albertini and Sontag E.D., Continuous control-Lyapunov functions for asymptotically controllable time-varying systems, Internat. J. Control. to appear. (See also Control-Lyapunov functions for time-varying set stabilization, Proc. European Control Conf., Brussels, July 1997, Paper ECC515.)
  2. Z. Artstein, Stabilization with relaxed controls. Nonl. Anal. TMA 7 (1983) 1163-1173. [CrossRef] [MathSciNet]
  3. F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York (1998).
  4. F.H. Clarke, Yu.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control 42 (1997) 1394-1407. [CrossRef] [MathSciNet]
  5. F.H. Clarke, Yu.S. Ledyaev, L. Rifford and R. Stern, Feedback stabilization and Lyapunov functions. preprint, Univ. de Lyon (1999).
  6. J.-M. Coron and L. Rosier, A relation between continuous time-varying and discontinuous feedback stabilization. J. Math. Systems, Estimation, and Control 4 (1994) 67-84.
  7. J. Kurzweil, On the inversion of Ljapunov's second theorem on stability of motion. Amer. Math. Society Translations, Series 2 24 (1956) 19-77.
  8. Yu.S. Ledyaev and E.D. Sontag, A remark on robust stabilization of general asymptotically controllable systems, in Proc. Conf. on Information Sciences and Systems (CISS 97), John Hopkins University, Baltimore (1997) 246-251.
  9. Yu.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. J. Nonl. Anal. 37 (1999) 813-840. [CrossRef] [MathSciNet]
  10. Y. Lin, E.D. Sontag and Y. Wang, A smooth converse Lyapunov theorem for robust stability, SIAM J. Control Optim. 34 (1996) 124-160. [CrossRef] [MathSciNet]
  11. E.P. Ryan, On Brockett's condition for smooth stabilizability and its necessity in a context of nonsmooth feedback. SIAM J. Control Optim. 32 (1994) 1597-1604. [CrossRef] [MathSciNet]
  12. E.D. Sontag A Lyapunov-like characterization of asymptotic controllability. SIAM J. Control Optim. 21 (1983) 462-471.
  13. E.D. Sontag, Mathematical Control Theory, Deterministic Finite Dimensional Systems, Second Edition. Springer-Verlag, New York (1998).
  14. E.D. Sontag, Stability and stabilization: Discontinuities and the effect of disturbances, in Nonlinear Analysis, Differential Equations, and Control, Proc. NATO Advanced Study Institute, Montreal, Jul/Aug 1998; F.H. Clarke and R.J. Stern, Eds., Kluwer, Dordrecht (1999) 551-598. See also Nonlinear Control Abstracts #NCA-8-2-981026, Oct 1998.
  15. E.D. Sontag and H.J. Sussmann, Nonsmooth Control Lyapunov Functions, in Proc. IEEE Conf. Decision and Control, New Orleans, IEEE Publications (1995) 2799-2805.