Hamiltonian matrices for lifted systems and periodic Riccati equations in H2/H∞ analysis and control

Results relative to the H₂ and H_∞ analysis and control of a periodic system are stated in terms of general relationships between periodic and algebraic Riccati equations. The time-invariant representation of a periodic system is introduced and successively used to build up the adjoint input-output operator of the original system. This leads to the formulation of a natural correspondence between general-type periodic Riccati equations associated with the periodic system and algebraic Riccati equations associated with its shift-invariant representation. It turns out that the periodic generators of the periodic Riccati equations associated with the original periodic system satisfy the difference Riccati equation associated with its time-invariant reformulation. This fact originates a number of fairly interesting results on the specific Riccati equations that are encountered in analysis and control of linear systems. In this way, results for H₂ and H_∞ analysis and control are provided