Continuous-time periodic systems in H2 and H∞ part I:: Theoretical aspects

The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of H-2 and H-infinity norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in H-2 and H-infinity are introduced and solved.