Algebraic Riccati equations and infinitesimal V-stability, a Grobner basis approach

We investigate the connection between infinitesimal V-stability of solutions to the algebraic Riccati equations, the Hamiltonian eigenstructure of the solutions, and the quadratic differential of the corresponding Riccati map. Infinitesimal V-stability of critical points of the Riccati map is crucially related to stability of the Riccati map and characterizes the behavior of these solutions under perturbations of problem data. Grobner bases are used to implement the calculations.