• Proof Using the partitioned
equation 0=AP+PA*+BB*
to get
• A11P1+P1A11*+B1B1*=0, P1A21*+B1B2*=0, and B2B2*=0
• then we
conclude that B2 = 0 and A21 = 0. Hence, part of the realization is not
controllable:
•
•
• P1>0 if A11 is stable. So (A11, B1) is controllable.
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