Homotopy methods for the solution of general modified algebraic Riccati equations

In the paper, the authors present a method for the numerical solution of modified algebraic Riccati equations, A^T Q+QA-Q Sigma Q+V+F(Q)=0, where the perturbation term F is low rank. They use a continuous homotopy approach with discrete corrections at each homotopy step. Their algorithm requires the solution of several perturbed Lyapunov equations during each iteration; thus they also address the rapid solution of sets of perturbed Lyapunov equations.