On Optimal Feedback Control for Stationary Linear Systems

We study linear-quadratic optimal control problems for finite dimensional stationary linear systems A X + B U = Z with output Y = C X + D U from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.