Free access
Issue
ESAIM: COCV
Volume 15, Number 3, July-September 2009
Page(s) 599 - 625
DOI http://dx.doi.org/10.1051/cocv:2008046
Published online 19 July 2008
  1. F. Albertini and E.D. Sontag, Continuous control-Lyapunov functions for asymptotic controllable time-varying systems. Int. J. Control 72 (1990) 1630–1641. [CrossRef]
  2. Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. Theory Methods Appl. 7 (1983) 1163–1173. [CrossRef] [MathSciNet]
  3. A. Bacciotti and L. Rosier, Liapunov Functions and Stability in Control Theory, Lecture Notes in Control and Information Sciences 267. Springer-Verlag, London (2001).
  4. F.H. Clarke and R.J. Stern, State constrained feedback stabilization. SIAM J. Contr. Opt. 42 (2003) 422–441. [CrossRef]
  5. F.H. Clarke, Y.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Contr. 42 (1997) 1394–1407. [CrossRef] [MathSciNet]
  6. F.H. Clarke, Y.S. Ledyaev, L. Rifford and R.J. Stern, Feedback stabilization and Lyapunov functions. SIAM J. Contr. Opt. 39 (2000) 25–48. [CrossRef] [MathSciNet]
  7. J.-M. Coron and L. Rosier, A relation between continuous time-varying and discontinuous feedback stabilization. J. Math. Syst. Estim. Control 4 (1994) 67–84.
  8. A.V. Fillipov, Differential Equations with Discontinuous Right-Hand Sides. Kluwer Academic Publishers (1988).
  9. R.A. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design- State Space and Lyapunov Techniques. Birkhauser, Boston (1996).
  10. J.G. Hocking and G.S. Young, Topology. Dover Editions (1988).
  11. I. Karafyllis, Necessary and sufficient conditions for the existence of stabilizing feedback for control systems. IMA J. Math. Control Inf. 20 (2003) 37–64. [CrossRef]
  12. I. Karafyllis, Non-uniform in time robust global asymptotic output stability. Systems Control Lett. 54 (2005) 181–193. [CrossRef] [MathSciNet]
  13. I. Karafyllis and C. Kravaris, Robust output feedback stabilization and nonlinear observer design. Systems Control Lett. 54 (2005) 925–938. [CrossRef] [MathSciNet]
  14. I. Karafyllis and J. Tsinias, A converse Lyapunov theorem for non-uniform in time global asymptotic stability and its application to feedback stabilization. SIAM J. Contr. Opt. 42 (2003) 936–965. [CrossRef]
  15. M. Krichman, A Lyapunov approach to detectability of nonlinear systems. Dissertation thesis, Rutgers University, Department of Mathematics, USA (2000).
  16. Y.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. Nonlinear Anal. Theory Methods Appl. 37 (1999) 813–840. [CrossRef] [MathSciNet]
  17. Y. Lin, E.D. Sontag and Y. Wang, A smooth converse Lyapunov theorem for robust stability. SIAM J. Contr. Opt. 34 (1996) 124–160. [CrossRef] [MathSciNet]
  18. J. Peuteman and D. Aeyels, Averaging results and the study of uniform asymptotic stability of homogeneous differential equations that are not fast time-varying. SIAM J. Contr. Opt. 37 (1999) 997–1010. [CrossRef]
  19. L. Rifford, Existence of Lipschitz and semiconcave control-Lyapunov functions. SIAM J. Contr. Opt. 39 (2000) 1043–1064. [CrossRef] [MathSciNet]
  20. L. Rifford, On the existence of nonsmooth control-Lyapunov function in the sense of generalized gradients. ESAIM: COCV 6 (2001) 593–612. [CrossRef] [EDP Sciences]
  21. E.D. Sontag, A universal construction of Artstein's theorem on nonlinear stabilization. Systems Control Lett. 13 (1989) 117–123. [CrossRef] [MathSciNet]
  22. E.D. Sontag, Clocks and insensitivity to small measurement errors. ESAIM: COCV 4 (1999) 537–557. [CrossRef] [EDP Sciences]
  23. E.D. Sontag and Y. Wang, Notions of input to output stability. Systems Control Lett. 38 (1999) 235–248. [CrossRef] [MathSciNet]
  24. E.D. Sontag and Y. Wang, Lyapunov characterizations of input-to-output stability. SIAM J. Contr. Opt. 39 (2001) 226–249. [CrossRef]
  25. A.R. Teel and L. Praly, A smooth Lyapunov function from a class-KL estimate involving two positive semidefinite functions. ESAIM: COCV 5 (2000) 313–367. [CrossRef] [EDP Sciences]
  26. J. Tsinias, A general notion of global asymptotic controllability for time-varying systems and its Lyapunov characterization. Int. J. Control 78 (2005) 264–276. [CrossRef]
  27. V.I. Vorotnikov, Partial Stability and Control. Birkhauser, Boston (1998).