1
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- Consider again the general framework with
- Suppose (A,B2) is stabilizable and (C2,A) is
detectable.
- Youla parameterization: all controllers K that internally stabilize G.
- Suppose GÎ RH¥ .
Then K=Q(I+G22Q)-1, Q Î RH¥ and
I+G22Q(¥ )
nonsingular.
- Proof: K stabilizes a stable plant G22 iff K(I-G22K)-1
is stable. So the conclusion follows by letting Q = K(I-G22K)-1.
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2
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- General Case: Let F and L be such that A+LC2 and A+B2F
are stable. Then K = Fl(J,Q):
- with any QÎ RH¥ and I+D22Q(¥ ) nonsingular.
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3
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- Closed-loop Matrix:
- Fl(G, K)= Fl(G, Fl(J, Q)) = Fl(T,
Q)
- = {T11+T12QT21: Q Î RH¥ and
I+G22Q(¥ )
nonsingular}.
- where T (T22=0) is given by
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4
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- Coprime Factorization Approach: Let be rcf
and lcf of G22 over RH¥ respectively. And let them satisfy the Bezout
identity:
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