Abstract
This dissertation is constituted of two parts. The first part treats of applications of the eigenspaces to finite dimensional linear time-invariant H-infinity control problems, while the second part concerns with the eigenspaces arising from discrete-time periodic linear systems. In the first part, we first analyze the structure of the stable invariant subspace of the related Hamiltonian matrix arising from the continuous-time H-infinity output feedback control problem. Then we consider numerical computation of the optimal H-infinity norms for both the continuous-time state feedback and output feedback control problems. With the same techniques, we finally consider in part one the more difficult problem of numerical computation of the optimal H-infinity norm for discrete-time linear time-invariant control systems. All are based on exploiting the eigenspaces. In the second part, we intuitively generalize the notion of eigenspaces to be applicable for regular periodic matrix pairs. We define the eigenvalues, eigenvectors, eigenspaces, and simple eigenspaces etc. for regular periodic matrix pairs. And we discuss the equivalences among their geometric form, algebraic form, and periodic block Schur form. Besides, we show several uniqueness properties to ensure the term "eigenspace" so defined.