# Clocks and Insensitivity to Small Measurement Errors

ESAIM: Control, Optimisation and Calculus of Variations (2010)

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

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topSontag, Eduardo D.. "Clocks and Insensitivity to Small Measurement Errors." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 537-557. <http://eudml.org/doc/116549>.

@article{Sontag2010,

abstract = {
This paper deals with the problem of stabilizing a system in the presence of
small measurement errors. It is known that, for general stabilizable systems,
there may be no possible memoryless state feedback which is robust with
respect to such errors. In contrast, a precise result is given here, showing
that, if a (continuous-time, finite-dimensional) system is stabilizable in any
way whatsoever (even by means of a dynamic, time varying, discontinuous,
feedback) then it can also be semiglobally and practically
stabilized in a way which is insensitive to
small measurement errors, by means of a hybrid strategy based on the idea of
sampling at a “slow enough” rate.
},

author = {Sontag, Eduardo D.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Control systems; feedback stabilization; controllability.; nonlinear control system; discontinuous feedback; piecewise constant feedback; Lyapunov function; sampling schedule; stabilization},

language = {eng},

month = {3},

pages = {537-557},

publisher = {EDP Sciences},

title = {Clocks and Insensitivity to Small Measurement Errors},

url = {http://eudml.org/doc/116549},

volume = {4},

year = {2010},

}

TY - JOUR

AU - Sontag, Eduardo D.

TI - Clocks and Insensitivity to Small Measurement Errors

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 4

SP - 537

EP - 557

AB -
This paper deals with the problem of stabilizing a system in the presence of
small measurement errors. It is known that, for general stabilizable systems,
there may be no possible memoryless state feedback which is robust with
respect to such errors. In contrast, a precise result is given here, showing
that, if a (continuous-time, finite-dimensional) system is stabilizable in any
way whatsoever (even by means of a dynamic, time varying, discontinuous,
feedback) then it can also be semiglobally and practically
stabilized in a way which is insensitive to
small measurement errors, by means of a hybrid strategy based on the idea of
sampling at a “slow enough” rate.

LA - eng

KW - Control systems; feedback stabilization; controllability.; nonlinear control system; discontinuous feedback; piecewise constant feedback; Lyapunov function; sampling schedule; stabilization

UR - http://eudml.org/doc/116549

ER -

## References

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- 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. Zbl0806.93049
- E.D. Sontag A Lyapunov-like characterization of asymptotic controllability. SIAM J. Control Optim.21 (1983) 462-471.
- E.D. Sontag, Mathematical Control Theory, Deterministic Finite Dimensional Systems, Second Edition. Springer-Verlag, New York (1998). Zbl0945.93001
- 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. Zbl0937.93034
- 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.

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