A stabilizing solution to the algebraic Riccati equation the resolvent method

A new approach to the problem of analytic representation of the stabilizing solution to the algebraic Riccati equation is proposed. The quadratic matrix equation is reduced to a linear one using the resolvent (sI _2n -H)^?1 of the Hamilton matrix. The symmetric solution to the obtained linear equation defines a stabilizing solution to the Riccati equation. Matrix coefficients of the linear equation are defined by the integral of resolvent in the complex domain over the closed contour which contains all its right poles. This construction of the solution to the problem gives rise to the development of important parts of the analysis and of the corresponding computing procedures.