• (a) Then the input/output
weighted Gramians P and Q are given by
wPA*+AP+BB*=0
wQ(A-BD-1C)+(A-BD-1C)*Q+C*(D-1)*D-1C=0
• (b) Suppose P and Q are
balanced:
• P=Q=S=diag (S1, S2)=diag (s1 Is1 ,…, sr Isr ,sr+1 Isr+1 , sN IsN)
q and let G be partitioned compatibly with S1, S2 as
q
q
q Then is stable and
minimum phase. Furthermore
•