Stabilizing controller for one linear discrete system with control constraints

This paper is devoted to the construction of a stabilizing controller in a discrete linear-quadratic stationary problem on a semiaxis with control constraints based on the extension principle. The asymptotic stability of the equilibrium point of the corresponding closed-loop system is established with the help of Malkin–Masser–Chetaev theorem. The results of numerical experiments demon-strating the obtained theoretical results are presented.