On the theory of constructive construction of a linear controller

The classical problem of stationary stabilization with respect to the state of a linear stationary control system is investigated. Efficient, easily algorithmic methods for constructing controllers of controlled systems are considered: the method of V. I. Zubov and the method of P. Brunovsky. The most successful modifications are indicated to facilitate the construction of a linear controller. A new modification of the construction of a linear regulator is proposed using the transformation of the matrix of the original system into a block-diagonal form. This modification contains all the advantages of both V. I. Zubov's method and P. Brunovsky's method, and allows one to reduce the problem with multidimensional control to the problem of stabilizing a set of independent subsystems with scalar control for each subsystem.