### Abstract

Original language | English |
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Title of host publication | Variable-Structure Systems and Sliding-Mode Control |

Subtitle of host publication | From Theory to Practice |

Publisher | Springer International |

Chapter | 3 |

Pages | 73-123 |

ISBN (Electronic) | 978-3-030-36621-6 |

ISBN (Print) | 978-3-030-36620-9 |

DOIs | |

Publication status | Published - 2020 |

### Publication series

Name | Studies in Systems, Decision and Control |
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Publisher | Springer |

Volume | 271 |

ISSN (Print) | 2198-4182 |

### Fingerprint

### Cite this

*Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice*(pp. 73-123). (Studies in Systems, Decision and Control; Vol. 271). Springer International. https://doi.org/10.1007/978-3-030-36621-6_3

**Computing and Estimating the Reaching Time of the Super-Twisting Algorithm.** / Seeber, Richard.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

*Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice.*Studies in Systems, Decision and Control, vol. 271, Springer International, pp. 73-123. https://doi.org/10.1007/978-3-030-36621-6_3

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TY - CHAP

T1 - Computing and Estimating the Reaching Time of the Super-Twisting Algorithm

AU - Seeber, Richard

PY - 2020

Y1 - 2020

N2 - The super-twisting algorithm is a second order sliding mode algorithm that may be used either for control or for observation purposes. An important performance characteristic of this algorithm is the so-called reaching or convergence time, the time it takes for the controller to reach the sliding surface or for the estimates to converge. In this chapter, three techniques are discussed to estimate, i.e., upper-bound, and in some cases even compute this reaching time in the presence of additive perturbations, which are Hölder continuous in the state or Lipschitz continuous in the time. The first is obtained from an analytic computation of the unperturbed reaching time; the second is based on a family of quadratic Lyapunov functions; and the third is derived from a necessary and sufficient stability criterion. For each approach the range of permissible perturbations, its asymptotic properties with respect to parameters and perturbation bounds, and, when applicable, the selection of parameters is discussed. Numerical comparisons illustrate the results obtained with each approach.

AB - The super-twisting algorithm is a second order sliding mode algorithm that may be used either for control or for observation purposes. An important performance characteristic of this algorithm is the so-called reaching or convergence time, the time it takes for the controller to reach the sliding surface or for the estimates to converge. In this chapter, three techniques are discussed to estimate, i.e., upper-bound, and in some cases even compute this reaching time in the presence of additive perturbations, which are Hölder continuous in the state or Lipschitz continuous in the time. The first is obtained from an analytic computation of the unperturbed reaching time; the second is based on a family of quadratic Lyapunov functions; and the third is derived from a necessary and sufficient stability criterion. For each approach the range of permissible perturbations, its asymptotic properties with respect to parameters and perturbation bounds, and, when applicable, the selection of parameters is discussed. Numerical comparisons illustrate the results obtained with each approach.

U2 - 10.1007/978-3-030-36621-6_3

DO - 10.1007/978-3-030-36621-6_3

M3 - Chapter

SN - 978-3-030-36620-9

T3 - Studies in Systems, Decision and Control

SP - 73

EP - 123

BT - Variable-Structure Systems and Sliding-Mode Control

PB - Springer International

ER -