Free access
Issue
ESAIM: COCV
Volume 6, 2001
Page(s) 593 - 611
DOI http://dx.doi.org/10.1051/cocv:2001124
Published online 15 August 2002
  1. Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. 7 (1983) 1163-1173. [CrossRef] [MathSciNet]
  2. J.-P. Aubin, Viability theory. Birkhäuser Boston Inc., Boston, MA (1991).
  3. J.P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag (1984).
  4. J.P. Aubin and H. Frankowska, Set-valued analysis. Birkhäuser (1990).
  5. C.I. Byrnes and A. Isidori, New results and examples in nonlinear feedback stabilization. Systems Control Lett. 12 (1989) 437-442. [CrossRef] [MathSciNet]
  6. F.H. Clarke, Yu.S. Ledyaev, L. Rifford and R.J. Stern, Feedback stabilization and Lyapunov functions. SIAM J. Control Optim. 39 (2000) 25-48. [CrossRef] [MathSciNet]
  7. F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley-Interscience, New York (1983). Republished as Classics Appl. Math. 5 (1990).
  8. F.H. Clarke, Yu.S. Ledyaev and R.J. Stern, Asymptotic stability and smooth Lyapunov functions. J. Differential Equations 149 (1998) 69-114. [CrossRef] [MathSciNet]
  9. F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York, Grad. Texts in Math. 178 (1998).
  10. J.-M. Coron, On the stabilization of some nonlinear control systems: Results, tools, and applications, in Nonlinear analysis, differential equations and control (Montreal, QC, 1998). Kluwer Acad. Publ., Dordrecht (1999) 307-367.
  11. J.-M. Coron, Some open problems in control theory, in Differential geometry and control (Boulder, CO, 1997). Providence, RI, Amer. Math. Soc. (1999) 149-162.
  12. J.-M. Coron and L. Rosier, A relation between continuous time-varying and discontinuous feedback stabilization. J. Math. Systems Estim. Control 4 (1994) 67-84. [MathSciNet]
  13. K. Deimling, Multivalued Differential Equations. de Gruyter, Berlin (1992).
  14. A.F. Filippov, Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers (1988).
  15. R. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design. State-Space and Lyapunov Techniques. Birkhäuser (1996).
  16. R.A. Freeman and P.V. Kokotovic, Backstepping design with nonsmooth nonlinearities, in Proc. of the IFAC Nonlinear Control Systems design symposium. Tahoe City, California (1995).
  17. O. Hájek, Discontinuous differential equations. I, II. J. Differential Equations 32 (1979) 149-170, 171-185. [CrossRef] [MathSciNet]
  18. J.-B. Hiriart-Urruty and C. Imbert, Les fonctions d'appui de la jacobienne généralisée de Clarke et de son enveloppe plénière. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998) 1275-1278.
  19. N.N. Krasovskiĭ, Stability of motion. Applications of Lyapunov's second method to differential systems and equations with delay. Stanford University Press, Stanford, California (1963). Translated by J.L. Brenner.
  20. J. Kurzweil, On the inversion of Lyapunov's second theorem on stability of motion. Amer. Math. Soc. Transl. Ser. 2 24 (1956) 19-77.
  21. Yu.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. Nonlinear Anal. 37 (1999) 813-840. [CrossRef] [MathSciNet]
  22. 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]
  23. J.L. Massera, Contributions to stability theory. Ann. of Math. (2) 64 (1956) 182-206. [CrossRef] [MathSciNet]
  24. E. Michael, Continuous selections. I. Ann. of Math. (2) 63 (1956) 361-382. [CrossRef] [MathSciNet]
  25. L. Praly and A.R. Teel, On assigning the derivative of a disturbance attenuation clf, in Proc. of the 37th IEEE conference on decision and control. Tampa, Florida (1998).
  26. L. Rifford, Existence of Lipschitz and semiconcave control-Lyapunov functions. SIAM J. Control Optim. 39 (2000) 1043-1064. [CrossRef] [MathSciNet]
  27. L. Rosier, Étude de quelques problèmes de stabilisation, Ph.D. Thesis. ENS de Cachan (1993).
  28. E.D. Sontag, A ``universal'' construction of Artstein's theorem on nonlinear stabilization. Systems Control Lett. 13 (1989) 117-123. [CrossRef] [MathSciNet]
  29. E.D. Sontag, Mathematical Control Theory. Springer-Verlag, New York, Texts Appl. Math. 6 (1990) (Second Edition, 1998).
  30. E.D. Sontag, Stability and stabilization: Discontinuities and the effect of disturbances, in Nonlinear analysis, differential equations and control (Montreal, QC, 1998). Kluwer Acad. Publ., Dordrecht (1999) 551-598.
  31. A.R. Teel and L. Praly, A smooth Lyapunov function from a class- Formula estimate involving two positive semidefinite functions. ESAIM: COCV 5 (2000) 313-367. [CrossRef] [EDP Sciences]
  32. J. Tsinias, A Lyapunov description of stability in control systems. Nonlinear Anal. 13 (1989) 3-74.
  33. J. Tsinias, Sufficient Lyapunov-like conditions for stabilization. Math. Control Signals Systems 2 (1989) 343-357. [CrossRef] [MathSciNet]
  34. J. Tsinias, A local stabilization theorem for interconnected systems. Systems Control Lett. 18 (1992) 429-434. [CrossRef] [MathSciNet]
  35. J. Tsinias, An extension of Artstein's theorem on stabilization by using ordinary feedback integrators. Systems Control Lett. 20 (1993) 141-148. [CrossRef] [MathSciNet]