Upper bounds of a stabilizer order for linear finite-dimensional systems

The problem of stabilizing linear dynamic systems by a 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.