Chapter
11: Controller Parameterization

qConsider again the general framework with

q Suppose (*A,B**2*) is stabilizable and (*C**2**,A*) is detectable.

q**Youla parameterization: ***all controllers** **K that internally stabilize G.
*

qSuppose *G*Î *RH*¥ . Then *K=Q(I+G**22**Q)**-1*, *Q* Î *RH*¥ and *I+G**22**Q*(*¥** * ) nonsingular.

q**Proof:** K stabilizes a stable
plant *G**22* iff *K(I-G**22**K)**-1* is stable. So the conclusion follows by
letting *Q
= K(I-G**22**K)**-1*.