• Note that
•-QX1-A*X2=X2
H_
• Post-multiply the above
equation by x:
• (A*+lI)X2 x=0
• Recall that RX2x = 0, we have
•x*X2*[A+ l*I R]=0.
•
• (A,R) stabilizable Þ X2 x=0 Þ
• has full column rank,
which is a contradiction.
• (Þ ) H Î dom(Ric) Þ A+RX is stable Þ (A, R) is stabilizable.
•
•