### Abstract

This work considers small-time local controllability (STLC) of single and multiple-input systems, ẋ = f_{o}(x) + ∑_{i}^{m}=1 f_{i}u^{i} where f_{o}(x) contains homogeneous polynomials and f_{1}, ..., f_{m} are constant vector fields. For single-input systems, it is shown that even-degree homogeneity precludes STLC if the state dimension is larger than one. This, along with the obvious result that for odd-degree homogeneous systems STLC is equivalent to accessibility, provides a complete characterization of STLC for this class of systems. In the multiple-input case, transformations on the input space are applied to homogeneous systems of degree two, an example of this type of system being motion of a rigid-body in a plane. Such input transformations are related via consideration of a tensor on the tangent space to congruence transformation of a matrix to one with zeros on the diagonal. Conditions are given for successful neutralization of bad type (1, 2) brackets via congruence transformations.

Original language | English (US) |
---|---|

Pages (from-to) | 3971-3976 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 4 |

State | Published - Dec 1 2000 |

Event | 39th IEEE Confernce on Decision and Control - Sydney, NSW, Australia Duration: Dec 12 2000 → Dec 15 2000 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*4*, 3971-3976.

**On nonlinear controllability of homogeneous systems linear in control.** / Melody, J. W.; Başar, T.; Bullo, F.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, vol. 4, pp. 3971-3976.

}

TY - JOUR

T1 - On nonlinear controllability of homogeneous systems linear in control

AU - Melody, J. W.

AU - Başar, T.

AU - Bullo, F.

PY - 2000/12/1

Y1 - 2000/12/1

N2 - This work considers small-time local controllability (STLC) of single and multiple-input systems, ẋ = fo(x) + ∑im=1 fiui where fo(x) contains homogeneous polynomials and f1, ..., fm are constant vector fields. For single-input systems, it is shown that even-degree homogeneity precludes STLC if the state dimension is larger than one. This, along with the obvious result that for odd-degree homogeneous systems STLC is equivalent to accessibility, provides a complete characterization of STLC for this class of systems. In the multiple-input case, transformations on the input space are applied to homogeneous systems of degree two, an example of this type of system being motion of a rigid-body in a plane. Such input transformations are related via consideration of a tensor on the tangent space to congruence transformation of a matrix to one with zeros on the diagonal. Conditions are given for successful neutralization of bad type (1, 2) brackets via congruence transformations.

AB - This work considers small-time local controllability (STLC) of single and multiple-input systems, ẋ = fo(x) + ∑im=1 fiui where fo(x) contains homogeneous polynomials and f1, ..., fm are constant vector fields. For single-input systems, it is shown that even-degree homogeneity precludes STLC if the state dimension is larger than one. This, along with the obvious result that for odd-degree homogeneous systems STLC is equivalent to accessibility, provides a complete characterization of STLC for this class of systems. In the multiple-input case, transformations on the input space are applied to homogeneous systems of degree two, an example of this type of system being motion of a rigid-body in a plane. Such input transformations are related via consideration of a tensor on the tangent space to congruence transformation of a matrix to one with zeros on the diagonal. Conditions are given for successful neutralization of bad type (1, 2) brackets via congruence transformations.

UR - http://www.scopus.com/inward/record.url?scp=0034439886&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034439886&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0034439886

VL - 4

SP - 3971

EP - 3976

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -