Control affine systems on solvable three-dimensional Lie groups, I

Rory Biggs and Claudiu C. Remsing

Address: Department of Mathematics (Pure and Applied), Rhodes University, PO Box 94, 6140 Grahamstown, South Africa


Abstract: We seek to classify the full-rank left-invariant control affine systems evolving on solvable three-dimensional Lie groups. In this paper we consider only the cases corresponding to the solvable Lie algebras of types $\,II$, $\,IV$, and $\,V\,$ in the Bianchi-Behr classification.

AMSclassification: primary 93A10; secondary 93B27, 17B30.

Keywords: left-invariant control system, (detached) feedback equivalence, affine subspace, solvable Lie algebra.

DOI: 10.5817/AM2013-3-187