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

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

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

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topJammazi, 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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