Asymptotic expansion of a stabilizing solution of the Riccati algebraic equation (Q1593908)

The author describes an algorithm for constructing an asymptotic expansion to an antistabilizing solution \(X_0\) associated with a Riccati equation determined by the matrices \[ A= A_0+\varepsilon A_1,\quad Q= Q_0+ \varepsilon Q_1,\quad R= R_0+ \varepsilon R_1 \] assuming that for \(\varepsilon\neq 0\) sufficiently small there exists a stabilizing solution. The paper is recommended to those working with \(J\)-factorization of matrix polynomials with respect to the imaginary axis.