Equivalence of Control Systems on the Pseudo-Orthogonal Group SO (2, 1)₀

We consider left-invariant control affine systems on the matrix Lie group SO (2, 1)₀. A classification, under state space equivalence, of all such full-rank control systems is obtained. First, we identify certain subsets on which the group of Lie algebra automorphisms act transitively. We then systematically identify equivalence class representatives (for single-input, two-input and three-input control systems). A brief comparison of these classification results with existing results concludes the paper.