# Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm

Title | Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm |

Publication Type | Journal Article |

Year of Publication | 2013 |

Authors | Picó J, Picó-Marco E, Vignoni A, De Battista H |

Journal | Automatica |

Volume | 49 |

Pagination | 534 - 539 |

ISSN | 0967-0661 |

Keywords | Bioprocess control |

Abstract | The super-twisting algorithm (STA) has become the prototype of second-order sliding mode algorithm. It achieves finite time convergence by means of a continuous action, without using information about derivatives of the sliding constraint. Thus, chattering associated to traditional sliding-mode observers and controllers is reduced. The stability and finite-time convergence analysis have been jointly addressed from different points of view, most of them based on the use of scaling symmetries (homogeneity), or non-smooth Lyapunov functions. Departing from these approaches, in this contribution we decouple the stability analysis problem from that of finite-time convergence. A nonlinear change of coordinates and a time-scaling are used. In the new coordinates and timeâ€“space, the transformed system is stabilized using any appropriate standard design method. Conditions under which the combination of the nonlinear coordinates transformation and the time-scaling is a stability preserving map are given. Provided convergence in the transformed space is faster than O(1/T) -where T is the transformed time- convergence of the original system takes place in finite-time. The method is illustrated by designing a generalized super-twisting observer able to cope with a broad class of perturbations. |

URL | http://www.sciencedirect.com/science/article/pii/S0967066113000488 |

DOI | 10.1016/j.conengprac.2013.03.003 |