On nonlinear controllability of homogeneous systems linear in control

J. W. Melody, T. Başar, F. Bullo

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)3971-3976
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 2000
Event39th IEEE Confernce on Decision and Control - Sydney, NSW, Australia
Duration: Dec 12 2000Dec 15 2000

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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