### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 135-144 |

Number of pages | 10 |

Journal | Systems and control letters |

Volume | 27 |

Issue number | 27 |

DOIs | |

Publication status | Published - 1996 |

### Keywords

- METIS-140858
- IR-30218

### Cite this

*Systems and control letters*,

*27*(27), 135-144. https://doi.org/10.1016/0167-6911(95)00059-3

}

*Systems and control letters*, vol. 27, no. 27, pp. 135-144. https://doi.org/10.1016/0167-6911(95)00059-3

**Equivalence of nonlinear systems to triangular form: the singular case.** / Celikovsky, S.; Celikovsky, Sergej; Nijmeijer, Henk.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Equivalence of nonlinear systems to triangular form: the singular case

AU - Celikovsky, S.

AU - Celikovsky, Sergej

AU - Nijmeijer, Henk

PY - 1996

Y1 - 1996

N2 - The problem of state equivalence of a given nonlinear system to a triangular form is considered here. The solution of this problem has been known for the regular case, i.e. when there exists a certain nested sequence of regular and involutive distributions. It is also known that in this case the corresponding system is linearizable using a smooth coordinate change and static state feedback. This paper deals with the singular case, i.e. when the nested sequence of involutive distributions of the system contains singular distributions. Special attention is paid to the so-called bijective triangular form. Geometric, coordinates-free criteria for the solution of the above problem as well as constructive, verifiable procedures are given. These results are used to obtain a result in the nonsmooth stabilization problem.

AB - The problem of state equivalence of a given nonlinear system to a triangular form is considered here. The solution of this problem has been known for the regular case, i.e. when there exists a certain nested sequence of regular and involutive distributions. It is also known that in this case the corresponding system is linearizable using a smooth coordinate change and static state feedback. This paper deals with the singular case, i.e. when the nested sequence of involutive distributions of the system contains singular distributions. Special attention is paid to the so-called bijective triangular form. Geometric, coordinates-free criteria for the solution of the above problem as well as constructive, verifiable procedures are given. These results are used to obtain a result in the nonsmooth stabilization problem.

KW - METIS-140858

KW - IR-30218

U2 - 10.1016/0167-6911(95)00059-3

DO - 10.1016/0167-6911(95)00059-3

M3 - Article

VL - 27

SP - 135

EP - 144

JO - Systems and control letters

JF - Systems and control letters

SN - 0167-6911

IS - 27

ER -