Hamiltonian structure of the Algebraic Riccati Equation and its Infinitesimal V -Stability
نویسندگان
چکیده
We will investigate the stability behavior of quadratic maps in higher dimensions. To check stability, we will use infinitesimal V -stability of critical points of the map; since the infinitesimal V -stability of a map at all of its critical points is equivalent to the stability of the map. We will establish the connection between infinitesimal V-stability of solutions to the Algebraic Riccati Equations, and the Hamiltonian eigenstructure of the solutions, by investigating the stability behavior 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. Gröbner Bases are used to implement the calculations.
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