Solutions of polynomials for linear stationary system with conditions to state function and controllibility function

The aim of this article is to prove that, solution x(t) (state function) of the linear stationary dynamic system x(t) = Bx(t) + Du(t), which transfers the system from any initial conditions in to any final conditions and at the same time satisfies conditions given for the controllability function u(t) is possible to find in the type of polynomials of degree r + (k + 2)(p + 1)-1 with vector coefficients.