Open Access
Volume 28, 2022
Article Number 30
Number of page(s) 22
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. [CrossRef] [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. [CrossRef] [MathSciNet] [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. [CrossRef] [MathSciNet] [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. [CrossRef] [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. [CrossRef] [MathSciNet] [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, (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]

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