A discussion on the Hölder and robust finite-time partial stabilizability of Brockett’s integrator∗

Chaker Jammazi

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 2, page 360-382
  • ISSN: 1292-8119

Abstract

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We consider chained systems that model various systems of mechanical or biological origin. It is known according to Brockett that this class of systems, which are controllable, is not stabilizable by continuous stationary feedback (i.e. independent of time). Various approaches have been proposed to remedy this problem, especially instationary or discontinuous feedbacks. Here, we look at another stabilization strategy (by continuous stationary or discontinuous feedbacks) to ensure the asymptotic stability even in finite time for some variables, while other variables do converge, and not necessarily toward equilibrium. Furthermore, we build feedbacks that permit to vanish the two first components of the Brockett integrator in finite time, while ensuring the convergence of the last one. The considering feedbacks are continuous and discontinuous and regular outside zero.

How to cite

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Jammazi, Chaker. "A discussion on the Hölder and robust finite-time partial stabilizability of Brockett’s integrator∗." ESAIM: Control, Optimisation and Calculus of Variations 18.2 (2012): 360-382. <http://eudml.org/doc/276366>.

@article{Jammazi2012,
abstract = {We consider chained systems that model various systems of mechanical or biological origin. It is known according to Brockett that this class of systems, which are controllable, is not stabilizable by continuous stationary feedback (i.e. independent of time). Various approaches have been proposed to remedy this problem, especially instationary or discontinuous feedbacks. Here, we look at another stabilization strategy (by continuous stationary or discontinuous feedbacks) to ensure the asymptotic stability even in finite time for some variables, while other variables do converge, and not necessarily toward equilibrium. Furthermore, we build feedbacks that permit to vanish the two first components of the Brockett integrator in finite time, while ensuring the convergence of the last one. The considering feedbacks are continuous and discontinuous and regular outside zero. },
author = {Jammazi, Chaker},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Brockett’s integrator; discontinuous feedback law; finite-time partial stability; rational partial stability; robust control; Brockett's integrator},
language = {eng},
month = {7},
number = {2},
pages = {360-382},
publisher = {EDP Sciences},
title = {A discussion on the Hölder and robust finite-time partial stabilizability of Brockett’s integrator∗},
url = {http://eudml.org/doc/276366},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Jammazi, Chaker
TI - A discussion on the Hölder and robust finite-time partial stabilizability of Brockett’s integrator∗
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/7//
PB - EDP Sciences
VL - 18
IS - 2
SP - 360
EP - 382
AB - We consider chained systems that model various systems of mechanical or biological origin. It is known according to Brockett that this class of systems, which are controllable, is not stabilizable by continuous stationary feedback (i.e. independent of time). Various approaches have been proposed to remedy this problem, especially instationary or discontinuous feedbacks. Here, we look at another stabilization strategy (by continuous stationary or discontinuous feedbacks) to ensure the asymptotic stability even in finite time for some variables, while other variables do converge, and not necessarily toward equilibrium. Furthermore, we build feedbacks that permit to vanish the two first components of the Brockett integrator in finite time, while ensuring the convergence of the last one. The considering feedbacks are continuous and discontinuous and regular outside zero.
LA - eng
KW - Brockett’s integrator; discontinuous feedback law; finite-time partial stability; rational partial stability; robust control; Brockett's integrator
UR - http://eudml.org/doc/276366
ER -

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