EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 6 (2001) ESAIM: COCV, 6 (2001) 593-611 References
Free Access
Issue
ESAIM: COCV
Volume 6, 2001
Page(s) 593 - 611
DOI https://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] [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.