• (v) ||D||< g and there exists an X³0 such that
•X(A+BR-1D*C)+(A+BR-1D*C)*X+XBR-1B*X+C*(I+DR-1D*)C=0
• and A+BR-1D*C+BR-1B*X has no eigenvalues on the imaginary
axis.
• (vi) ||D||< g and there exists an X > 0 such that
•X(A+BR-1D*C)+(A+BR-1D*C)*X+XBR-1B*X+C*(I+DR-1D*)C<0
• (vii) there exists and X > 0 such that
•
•
qProof: We have already known: (i) Û (ii). (iii) Þ (ii) is obvious. To show that (ii) Þ (iii), we need to
show that (A+BR-1D*C, BR-1B*) is stabilizable (Theorem 12.2). In fact, we will show that A+BR-1D*C is stable for all those g such that ||G||¥ < g .
q