Free Access
Issue
ESAIM: COCV
Volume 15, Number 3, July-September 2009
Page(s) 599 - 625
DOI https://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] [Google Scholar]
  2. Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. Theory Methods Appl. 7 (1983) 1163–1173. [CrossRef] [MathSciNet] [Google Scholar]
  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). [Google Scholar]
  4. F.H. Clarke and R.J. Stern, State constrained feedback stabilization. SIAM J. Contr. Opt. 42 (2003) 422–441. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  8. A.V. Fillipov, Differential Equations with Discontinuous Right-Hand Sides. Kluwer Academic Publishers (1988). [Google Scholar]
  9. R.A. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design- State Space and Lyapunov Techniques. Birkhauser, Boston (1996). [Google Scholar]
  10. J.G. Hocking and G.S. Young, Topology. Dover Editions (1988). [Google Scholar]
  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] [Google Scholar]
  12. I. Karafyllis, Non-uniform in time robust global asymptotic output stability. Systems Control Lett. 54 (2005) 181–193. [CrossRef] [MathSciNet] [Google Scholar]
  13. I. Karafyllis and C. Kravaris, Robust output feedback stabilization and nonlinear observer design. Systems Control Lett. 54 (2005) 925–938. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  15. M. Krichman, A Lyapunov approach to detectability of nonlinear systems. Dissertation thesis, Rutgers University, Department of Mathematics, USA (2000). [Google Scholar]
  16. Y.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. Nonlinear Anal. Theory Methods Appl. 37 (1999) 813–840. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  19. L. Rifford, Existence of Lipschitz and semiconcave control-Lyapunov functions. SIAM J. Contr. Opt. 39 (2000) 1043–1064. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  21. E.D. Sontag, A universal construction of Artstein's theorem on nonlinear stabilization. Systems Control Lett. 13 (1989) 117–123. [CrossRef] [MathSciNet] [Google Scholar]
  22. E.D. Sontag, Clocks and insensitivity to small measurement errors. ESAIM: COCV 4 (1999) 537–557. [CrossRef] [EDP Sciences] [Google Scholar]
  23. E.D. Sontag and Y. Wang, Notions of input to output stability. Systems Control Lett. 38 (1999) 235–248. [CrossRef] [MathSciNet] [Google Scholar]
  24. E.D. Sontag and Y. Wang, Lyapunov characterizations of input-to-output stability. SIAM J. Contr. Opt. 39 (2001) 226–249. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  27. V.I. Vorotnikov, Partial Stability and Control. Birkhauser, Boston (1998). [Google Scholar]

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