Free Access
Volume 6, 2001
Page(s) 593 - 611
Published online 15 August 2002
  1. Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. 7 (1983) 1163-1173. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.-P. Aubin, Viability theory. Birkhäuser Boston Inc., Boston, MA (1991). [Google Scholar]
  3. J.P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag (1984). [Google Scholar]
  4. J.P. Aubin and H. Frankowska, Set-valued analysis. Birkhäuser (1990). [Google Scholar]
  5. C.I. Byrnes and A. Isidori, New results and examples in nonlinear feedback stabilization. Systems Control Lett. 12 (1989) 437-442. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  7. F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley-Interscience, New York (1983). Republished as Classics Appl. Math. 5 (1990). [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  13. K. Deimling, Multivalued Differential Equations. de Gruyter, Berlin (1992). [Google Scholar]
  14. A.F. Filippov, Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers (1988). [Google Scholar]
  15. R. Freeman and P.V. Kokotovic, Robust Nonlinear Control Design. State-Space and Lyapunov Techniques. Birkhäuser (1996). [Google Scholar]
  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). [Google Scholar]
  17. O. Hájek, Discontinuous differential equations. I, II. J. Differential Equations 32 (1979) 149-170, 171-185. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  21. Yu.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. Nonlinear Anal. 37 (1999) 813-840. [Google Scholar]
  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] [Google Scholar]
  23. J.L. Massera, Contributions to stability theory. Ann. of Math. (2) 64 (1956) 182-206. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Michael, Continuous selections. I. Ann. of Math. (2) 63 (1956) 361-382. [Google Scholar]
  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). [Google Scholar]
  26. L. Rifford, Existence of Lipschitz and semiconcave control-Lyapunov functions. SIAM J. Control Optim. 39 (2000) 1043-1064. [CrossRef] [MathSciNet] [Google Scholar]
  27. L. Rosier, Étude de quelques problèmes de stabilisation, Ph.D. Thesis. ENS de Cachan (1993). [Google Scholar]
  28. E.D. Sontag, A ``universal'' construction of Artstein's theorem on nonlinear stabilization. Systems Control Lett. 13 (1989) 117-123. [CrossRef] [MathSciNet] [Google Scholar]
  29. E.D. Sontag, Mathematical Control Theory. Springer-Verlag, New York, Texts Appl. Math. 6 (1990) (Second Edition, 1998). [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  32. J. Tsinias, A Lyapunov description of stability in control systems. Nonlinear Anal. 13 (1989) 3-74. [Google Scholar]
  33. J. Tsinias, Sufficient Lyapunov-like conditions for stabilization. Math. Control Signals Systems 2 (1989) 343-357. [Google Scholar]
  34. J. Tsinias, A local stabilization theorem for interconnected systems. Systems Control Lett. 18 (1992) 429-434. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]

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