EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 28 (2022) ESAIM: COCV, 28 (2022) 30 References
Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 30
Number of page(s) 22
DOI https://doi.org/10.1051/cocv/2022022
Published online 25 May 2022
  1. Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. 7 (1983) 1163–1173. [CrossRef] [MathSciNet] [Google Scholar]
  2. U. Boscain and B. Piccoli, Optimal Syntheses for Control Systems on 2-D Manifolds. Springer (2004). [Google Scholar]
  3. P. Braun, L. Grüne, C.M. Kellett, Complete instability of differential inclusions using Lyapunov methods. IEEE Conf. Decis. Control (2018) 718–724. [Google Scholar]
  4. R.W. Brockett, Asymptotic stability and feedback stabilization. Differ. Geometr. Control Theory 27 (1983) 181–191. [Google Scholar]
  5. C.I. Byrnes, On Brockett’s necessary condition for stabilizability and the topology of Lyapunov functions on. Commun. Inf. Syst. 8 (2008) 333–352. [CrossRef] [MathSciNet] [Google Scholar]
  6. B.A. Christopherson, F. Jafari and B.S. Mordukhovich, A variational approach to local asymptotic and exponential stabilization of nonlinear systems. SN Operat. Res. Forum (2020) DOI: 10.1007/s43069-020-0003-z. [Google Scholar]
  7. F. Clarke, Lyapunov functions and discontinuous stabilizing feedback. Annu. Rev. Control 35 (2011) 13–33. [CrossRef] [Google Scholar]
  8. J.M. Coron, A necessary condition for feedback stabilization. Syst. Control Lett. 14 (1990) 227–232. [Google Scholar]
  9. J.M. Coron, Control and Nonlinearity. American Mathematical Society (2007). [Google Scholar]
  10. E.P. Ryan, On Brockett’s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback. SIAM J. Control Optim. 32 (1994) 1597–1604. [Google Scholar]
  11. R. Gupta, F. Jafari, R.J. Kipka and B.S. Mordukhovich, Linear openness and feedback stabilization of nonlinear control systems. Disc. Cont. Dyn. Systs. Ser. S 11 (2018) 1103–1119. [Google Scholar]
  12. R. Goebel, C. Prieur and A.R. Teel, Smooth patchy control Lyapunov functions. Automatica 45 (2009) 675–683. [CrossRef] [MathSciNet] [Google Scholar]
  13. H. Hermes, Asymptotically stabilizing feedback controls and the nonlinear regulator problem. SIAM J. Control Optim. 29 (1991) 185–196. [Google Scholar]
  14. C. Jammazi, M. Zaghdoudi and M. Boutayeb, On the global polynomial stabilization of nonlinear dynamical systems. Nonlinear Anal.: Real World Appl. 46 (2019) 29–42. [CrossRef] [MathSciNet] [Google Scholar]
  15. K. Jittorntrum, An implicit function theorem. J. Optim. Theory Appl. 25 (1978) 575–577. [CrossRef] [MathSciNet] [Google Scholar]
  16. S. Kumagai, An implicit function theorem: comment. J. Optim. Theory Appl. 31 (1980) 285–288. [CrossRef] [MathSciNet] [Google Scholar]
  17. G.A. Lafferriere and E.D. Sontag, Remarks on control lyapunov functions for discontinuous stabilizing feedback. Proc. 32nd IEEE Conf. Decis. Control (1993) 306–308. [Google Scholar]
  18. Y.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. Nonlinear Anal. 37 (1999) 813–840. [CrossRef] [MathSciNet] [Google Scholar]
  19. B.S. Mordukhovich, Variational Analysis and Applications. Springer (2018). [Google Scholar]
  20. S.M. Onishchenko, To the problem of the nonlinear systems stabilizability. J. Autom. Inf. Sci. 43 (2011) 1–12. [CrossRef] [Google Scholar]
  21. S.M. Onishchenko, Analysis of the conditions of controllability and stabilizability of nonlinear dynamical systems. J. Autom. Inf. Sci. 43 (2011) 10–22. [CrossRef] [Google Scholar]
  22. E.P. Ryan, On Brockett’s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback. SIAM J. Control Optim. 32 (1994) 1597–1604. [Google Scholar]
  23. T. Sadikhov and W.M. Haddad, A universal feedback controller for discontinuous dynamical systems using nonsmooth control Lyapunov functions. J. Dyn. Syst. Measur. Control 137 (2015) 041005. [CrossRef] [Google Scholar]
  24. U. Schreiber, M.S. New and T. Bartels, Saturated Subset. nLab, http://ncatlab.org/nlab/show/saturatedTsubset (version: 2017-05-21). [Google Scholar]
  25. E.D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems. Springer (1998). [Google Scholar]
  26. H.J. Sussmann, E.D. Sontag and D.Y. Yang, A general result on the stabilization of linear systems using bounded controls. IEEE Trans. Automat. Control 39 (1994) 2411–2425. [CrossRef] [MathSciNet] [Google Scholar]
  27. E.D. Sontag, Stability and stabilization: discontinuities and the effect of disturbances. In: Nonlinear Anal. Differ. Equ. Control, NATO Science Series 528. Springer, Dordrecht (1999) 551–598. [Google Scholar]
  28. S. Willard, General Topology. Courier Corporation (2004). [Google Scholar]
  29. J. Zabczyk, Some comments on stabilizability. J. Appl. Math. Optim. 19 (1989) 1–9. [CrossRef] [Google Scholar]
  30. V.I. Zubov, Methods of A.M. Lyapunov and Their Applications. Edited by P. Noordhoff (1964). [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.