Clocks and insensitivity to small measurement errors

Eduardo D. Sontag

ESAIM: Control, Optimisation and Calculus of Variations (1999)

  • Volume: 4, page 537-557
  • ISSN: 1292-8119

How to cite

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Sontag, Eduardo D.. "Clocks and insensitivity to small measurement errors." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 537-557. <http://eudml.org/doc/90553>.

@article{Sontag1999,
author = {Sontag, Eduardo D.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {nonlinear control system; discontinuous feedback; piecewise constant feedback; Lyapunov function; sampling schedule; stabilization},
language = {eng},
pages = {537-557},
publisher = {EDP Sciences},
title = {Clocks and insensitivity to small measurement errors},
url = {http://eudml.org/doc/90553},
volume = {4},
year = {1999},
}

TY - JOUR
AU - Sontag, Eduardo D.
TI - Clocks and insensitivity to small measurement errors
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1999
PB - EDP Sciences
VL - 4
SP - 537
EP - 557
LA - eng
KW - nonlinear control system; discontinuous feedback; piecewise constant feedback; Lyapunov function; sampling schedule; stabilization
UR - http://eudml.org/doc/90553
ER -

References

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  1. [1] F. Albertini and Sontag E.D., Continuous control-Lyapunov fonctions for asymptotically controllable time-varying systems, Internat. J. Control. to appear. (See also Control-Lyapunov functions for time-varying set stabilization, Proc. European Control Conf., Brussels, July 1997, Paper ECC515.) Zbl0949.93035MR1733874
  2. [2] Z. Artstein, Stabilization with relaxed controls. Nonl. Anal. TMA 7 ( 1983) 1163-1173. Zbl0525.93053MR721403
  3. [3] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York ( 1998). Zbl1047.49500MR1488695
  4. [4] F.H. Clarke, Yu.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control 42 ( 1997) 1394-1407. Zbl0892.93053MR1472857
  5. [5] F.H. Clarke, Yu.S. Ledyaev, L. Rifford and R. Stern, Feedback stabilization and Lyapunov functions. preprint, Univ. de Lyon ( 1999). Zbl0961.93047MR1780907
  6. [6] J.-M. Coron and L. Rosier, A relation between continuous time-varying and discontinuous feedback stabilization. J. Math. Systems, Estimation, and Control 4 ( 1994) 67-84. Zbl0925.93827MR1298548
  7. [7] J. Kurzweil, On the inversion of Ljapunov's second theorem on stability of motion. Amer. Math. Society Translations, Series 2 24 ( 1956) 19-77. Zbl0127.30703
  8. [8] Yu.S. Ledyaev and E.D. Sontag, A remark on robust stabilization of general asymptotically controllable systems, in Proc. Conf. on Information Sciences and Systems (CISS 97), John Hopkins University, Baltimore ( 1997) 246-251. MR1430107
  9. [9] Yu.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. J. Nonl. Anal. 37 ( 1999) 813-840. Zbl0947.34054MR1695080
  10. [10] Y. Lin, E.D. Sontag and Y. Wang, A smooth converse Lyapunov theorem for robust stability, SIAM J. Control Optim. 34 ( 1996) 124-160. Zbl0856.93070MR1372908
  11. [11] 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. Zbl0806.93049MR1297100
  12. [12] E.D. Sontag A Lyapunov-like characterization of asymptotic controllability. SIAM J. Control Optim. 21 ( 1983) 462-471. Zbl0513.93047MR696908
  13. [13] E.D. Sontag, Mathematical Control Theory, Deterministic Finite Dimensional Systems, Second Edition. Springer-Verlag, New York ( 1998). Zbl0945.93001MR1640001
  14. [14] E.D. Sontag, Stability and stabilization: Discontinuities and the effect of disturbances, in Nonlinear Analysis, Differential Equations, and Control, Proc. NATO Advanced Study Institute, Montreal, Jul/Aug 1998; F.H. Clarke and R.J. Stern, Eds., Kluwer, Dordrecht ( 1999) 551-598. See also Nonlinear Control Abstracts #NCA-8-2-981026, Oct 1998. Zbl0937.93034MR1695014
  15. [15] E.D. Sontag and H.J. Sussmann, Nonsmooth Control Lyapunov Functions, in Proc. IEEE Conf. Decision and Control, New Orleans, IEEE Publications ( 1995) 2799-2805. 

Citations in EuDML Documents

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  1. Rafal Goebel, Andrew R. Teel, Direct design of robustly asymptotically stabilizing hybrid feedback
  2. Iasson Karafyllis, John Tsinias, Control Lyapunov functions and stabilization by means of continuous time-varying feedback
  3. Iasson Karafyllis, John Tsinias, Control Lyapunov functions and stabilization by means of continuous time-varying feedback
  4. Ludovic Rifford, Stratified semiconcave control-Lyapunov functions and the stabilization problem
  5. Francis H. Clarke, Ludovic Rifford, R. J. Stern, Feedback in state constrained optimal control
  6. Francis H. Clarke, Ludovic Rifford, R. J. Stern, Feedback in state constrained optimal control

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