##
**Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems.**
*(English)*
Zbl 1244.93142

Summary: Finite-time stabilization is considered for a class of nonlinear systems dominated by a lower-triangular model with a time-varying gain. Based on the finite-time Lyapunov stability theorem and dynamic gain control design approach, state feedback finite-time stabilization controllers are proposed with gains being tuned online by two dynamic equations. Different from many existing finite-time control designs for lower-triangular nonlinear systems, the celebrated backstepping method is not utilized here. It is observed that our design procedure is much simpler, and the resulting control gains are in general not as high as those provided by the backstepping method. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

### MSC:

93D15 | Stabilization of systems by feedback |

93C10 | Nonlinear systems in control theory |

93C15 | Control/observation systems governed by ordinary differential equations |

Full Text:
DOI

### References:

[1] | Bhat, S. P.; Bernstein, D. S., Finite-time stability of continuous autonomous systems, SIAM Journal on Control and Optimization, 38, 3, 751-766 (2000) · Zbl 0945.34039 |

[2] | Chen, Z., & Huang, J. (2004). Global output feedback stabilization for uncertain nonlinear systems with output dependent incremental rate. In Proceedings of the American control conference. Boston, Massachusetts; Chen, Z., & Huang, J. (2004). Global output feedback stabilization for uncertain nonlinear systems with output dependent incremental rate. In Proceedings of the American control conference. Boston, Massachusetts |

[3] | Feng, Y.; Yu, X.; Man, Z., Non-singular terminal sliding mode control of rigid manipulators, Automatica, 38, 12, 2159-2167 (2002) · Zbl 1015.93006 |

[4] | Haddad, W. M., Nersesov, S. G., & Du, L. (2008). Finite-time stability for time-varying nonlinear dynamical systems. In American control conference. Westin Seattle Hotel, Seattle, Washington, USA; Haddad, W. M., Nersesov, S. G., & Du, L. (2008). Finite-time stability for time-varying nonlinear dynamical systems. In American control conference. Westin Seattle Hotel, Seattle, Washington, USA |

[5] | Hong, Y.; Jiang, Z., Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties, IEEE Transactions on Automatic Control, 51, 12, 1950-1956 (2006) · Zbl 1366.93577 |

[6] | Hong, Y.; Wang, J.; Cheng, D., Adaptive finite-time control of nonlinear systems with parametric uncertainty, IEEE Transactions on Automatic Control, 51, 5, 858-862 (2006) · Zbl 1366.93290 |

[7] | Huang, X.; Lin, W.; Yang, B., Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica, 41, 5, 881-888 (2005) · Zbl 1098.93032 |

[8] | Krishnamurthy, P.; Khorrami, F., On uniform solvability of parameter-dependent Lyapunov inequalities and applications to various problems, SIAM Journal on Control and Optimization, 45, 4, 1147-1164 (2006) · Zbl 1115.93029 |

[9] | Lee, S. H., Park, J. B., & Choi, Y. H. (2009). Finite time control of nonlinear underactuated systems using terminal sliding surface. In IEEE international symposium on industrial electronics. Seoul Olympic Parktel, Seoul, Korea; Lee, S. H., Park, J. B., & Choi, Y. H. (2009). Finite time control of nonlinear underactuated systems using terminal sliding surface. In IEEE international symposium on industrial electronics. Seoul Olympic Parktel, Seoul, Korea |

[10] | Lei, H.; Lin, W., Robust control of uncertain systems with polynomial nonlinearity by output feedback, International Journal of Robust and Nonlinear Control, 19, 6, 692-723 (2009) · Zbl 1169.93322 |

[11] | Pongvuthithum, R., A time-varying feedback approach for triangular systems with nonlinear parameterization, SIAM Journal on Control and Optimization, 48, 3, 1660-1674 (2009) · Zbl 1282.93129 |

[12] | Praly, L.; Jiang, Z., Linear output feedback with dynamic high gain for nonlinear systems, Systems & Control Letters, 53, 2, 107-116 (2004) · Zbl 1157.93494 |

[13] | Seo, S., Shim, H., & Seo, J. H. (2008). Global finite-time stabilization of a nonlinear system using dynamic exponent scaling. In Proceedings of the 47th IEEE conference on decision and control. Cancun, Mexico; Seo, S., Shim, H., & Seo, J. H. (2008). Global finite-time stabilization of a nonlinear system using dynamic exponent scaling. In Proceedings of the 47th IEEE conference on decision and control. Cancun, Mexico |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.