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1 results

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

  • Chaker Jammazi
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 18 / Issue 2 / April 2012
    Published online by Cambridge University Press:
    13 April 2011, pp. 360-382
    Print publication:
    April 2012

  • We consider chained systems that model various systems of mechanical or biologicalorigin. It is known according to Brockett that this class of systems, which arecontrollable, is not stabilizable by continuous stationary feedback (i.e.independent of time). Various approaches have been proposed to remedy thisproblem, especially instationary or discontinuous feedbacks. Here, we look at anotherstabilization strategy (by continuous stationary or discontinuous feedbacks) to ensure theasymptotic stability even in finite time for some variables, while other variables doconverge, and not necessarily toward equilibrium. Furthermore, we build feedbacks thatpermit to vanish the two first components of the Brockett integrator in finite time, whileensuring the convergence of the last one. The considering feedbacks are continuous anddiscontinuous and regular outside zero.