Computing L2 and H2 Norms
§Let G(s) Î L2 and g(t) = L-1 [G(s)]. Then
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• 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.