q Now assume We=wsI, Wd=I, W1=I, W2=wtI and P is stable and has a stable inverse (I.e.,
minimum phase) and K(s)=P-1(s)l(s) such that K(s) is proper and the
closed-loop is stable. Then
qSo =
Si =1/(1+l(s))I=e(s)I, To = Ti
=l(s)/(1+l(s))I=t(s)I
•
• and
•
• Let the SVD of P(jw) be
•P(jw)=USV*, S = diag(s1, s2 , …, sm)
• with and where m is the dimension of P.
• Then
q
q