Algorithms of constructing a stabilizing solution of the algebraic Riccati equation based on its linear reduction in the problems of analytical construction of controllers

In the problem of the stabilizing solution of the algebraic Riccati equation, the resolvent Θ(s) = (s I _2n ? H)^?1 of the Hamilton 2n × 2n-matrix H of the algebraic Riccati equation allows us to reduce the problem to a linear matrix equation. In 1], the constructions necessary for this and the theorem of existence and representation of the stabilized solutions to an algebraic Riccati equation was proposed. In this paper, the methods of constructing the resolvent and the linear reduction matrix defined by it necessary for the application of the theorem, and in addition, the algorithms of constructing stabilizing solution of the algebraic Riccati equation are proposed.