# Clocks and insensitivity to small measurement errors

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

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

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top## How to cite

topSontag, 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

top- [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] Z. Artstein, Stabilization with relaxed controls. Nonl. Anal. TMA 7 ( 1983) 1163-1173. Zbl0525.93053MR721403
- [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] 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] F.H. Clarke, Yu.S. Ledyaev, L. Rifford and R. Stern, Feedback stabilization and Lyapunov functions. preprint, Univ. de Lyon ( 1999). Zbl0961.93047MR1780907
- [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] 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] 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] Yu.S. Ledyaev and E.D. Sontag, A Lyapunov characterization of robust stabilization. J. Nonl. Anal. 37 ( 1999) 813-840. Zbl0947.34054MR1695080
- [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] 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] E.D. Sontag A Lyapunov-like characterization of asymptotic controllability. SIAM J. Control Optim. 21 ( 1983) 462-471. Zbl0513.93047MR696908
- [13] E.D. Sontag, Mathematical Control Theory, Deterministic Finite Dimensional Systems, Second Edition. Springer-Verlag, New York ( 1998). Zbl0945.93001MR1640001
- [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] 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

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

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