Upper bounds of a light stabilizer order for linear finite

The problem of light stabilizing linear dynamic systems by a light stabilizer (a dynamic system) is considered. The upper bounds of a stabilizer order obtained using two Hidenori Kimura results are studied. The bound k 0 is shown to be better than the bounds k 1 and k 2 only in one case. In addition, all possible relations between three bounds k 0, k 1, and k 2 are proven to be realized in the space of parameters of observability and controllability indices, i.e., there is a dynamic system with the respective observability and controllability indices.