We construct the concrete category LiCS of left-invariant control systems (on Lie groups) and point out some very basic properties. Mor-phisms in this category are examined briefly. Also, covering control systems are introduced and organized into a (comma) category associated with LiCS.
We consider left-invariant control affine systems evolving on Lie groups. In this context, feedback equivalence specializes to detached feedback equivalence. We characterize (local) detached feedback equivalence in a simple algebraic manner. We then classify all (full-rank) systems evolving on three-dimensional Lie groups. A representative is identified for… (More)