Input-to-state stability with respect to measurement disturbances for one-dimensional systems

Nicolas Chung Siong Fah

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

  • Volume: 4, page 99-121
  • ISSN: 1292-8119

Abstract

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We consider one-dimensional affine control systems. We show that if such a system is stabilizable by means of a continuous, time-invariant feedback, then it can be made input-to-state stable with respect to measurement disturbances, using a continuous, periodic time-varying feedback. We provide counter-examples showing that the result does not generally hold if we want the feedback to be time-invariant or if the control system is not supposed affine.

How to cite

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Nicolas Chung Siong Fah. "Input-to-state stability with respect to measurement disturbances for one-dimensional systems." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 99-121. <http://eudml.org/doc/197344>.

@article{NicolasChungSiongFah2010,
abstract = { We consider one-dimensional affine control systems. We show that if such a system is stabilizable by means of a continuous, time-invariant feedback, then it can be made input-to-state stable with respect to measurement disturbances, using a continuous, periodic time-varying feedback. We provide counter-examples showing that the result does not generally hold if we want the feedback to be time-invariant or if the control system is not supposed affine. },
author = {Nicolas Chung Siong Fah},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Input-to-state stability; stabilization; measurement errors.; input-to-state stability; one-dimensional systems; periodic feedback; measurement disturbances},
language = {eng},
month = {3},
pages = {99-121},
publisher = {EDP Sciences},
title = {Input-to-state stability with respect to measurement disturbances for one-dimensional systems},
url = {http://eudml.org/doc/197344},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Nicolas Chung Siong Fah
TI - Input-to-state stability with respect to measurement disturbances for one-dimensional systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 99
EP - 121
AB - We consider one-dimensional affine control systems. We show that if such a system is stabilizable by means of a continuous, time-invariant feedback, then it can be made input-to-state stable with respect to measurement disturbances, using a continuous, periodic time-varying feedback. We provide counter-examples showing that the result does not generally hold if we want the feedback to be time-invariant or if the control system is not supposed affine.
LA - eng
KW - Input-to-state stability; stabilization; measurement errors.; input-to-state stability; one-dimensional systems; periodic feedback; measurement disturbances
UR - http://eudml.org/doc/197344
ER -

References

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  8. J.M. Coron, On the stabilization of controllable and observable systems by an output feedback law. Math. Control Signals Systems7 (1994) 187-216.  Zbl0830.93064
  9. R. Freeman, Time-varying feedback for the global stabilization of nonlinear systems with measurement disturbances, in Proc. European Control Conference, Brussels (1997).  
  10. N.N. Krasovskii, Stability of motion, Standford University Press, Standford (1963).  Zbl0109.06001
  11. J.M. Coron, L. Praly and A. Teel, Feedback stabilization of nonlinear systems: sufficient conditions and Lyapynov and Input-output techniques, in Trends in Control, A. Isidori Ed., Springer-Verlag (1995) 293-348.  
  12. E.D. Sontag and Y. Wang, New characterizations of the input to state stability property. IEEE Trans. Automat. Contr.41 (1996) 1283-1294.  Zbl0862.93051
  13. Y. Lin, Input-to-state stability for noncompact sets Proc. 13th IFAC World Congress, Vol. E, San Francisco (1996) 73-78.  

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