Computing
L2 and H2 Norms
§Let G(s) Î L2 and g(t) = L-1 [G(s)]. Then
Consider G(s)=C(sI-A)-1B Î RH2 . Then
we have
||G(s)||22= trace(B*L0B) = trace(CLcC*)
where L0 and Lc are
observability and controllability Gramians:
ALc+LcA*+BB* = 0
A*L0+L0A+C*C = 0.
