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296 H LOOP SHAPING 22 Figure 16.1:Left Coprime Factor Perturbed Systems Suppose P has a stabilizable and detectable state space realization given by B and let L be a matrix such that A+LC is stable then a left coprime factorization of P=MI-N is given by [=[ B+LD L ZC ZD Z where Z can be any nonsingular matrix. In particular,we shall choose Z =(I+ DD*)1-2if P=MI-Nis chosen to be a normalized left coprime factorization.Denote K=/K then the system diagram can be put in an LFT form as in Figure 16.2 with the gener- alized plant 以，aT可 ty A D_D-2 C2 D2-D22 To apply the Hoo control formulae in Chapter 14,we need to normalize the "D_2" matrix first.Note that []-[r+ro明o-[4o (I+DD)1÷ EDI+DD)1÷ H LOOP SHAPING f f f y w z z r M M N N K Figure Left Coprime Factor Perturbed Systems Suppose P has a stabilizable and detectable state space realization given by P A B C D and let L be a matrix such that A LC is stable then a left coprime factorization of P M N is given by h N M i A LC B LD L ZC ZD Z where Z can be any nonsingular matrix In particular we shall choose Z I DD if P M N is chosen to be a normalized left coprime factorization Denote K K then the system diagram can be put in an LFT form as in Figure with the gener alized plant Gs M I P M P A LZ B C Z I D C Z D A B B C D D C D D To apply the H control formulae in Chapter we need to normalize the D matrix rst Note that I D U I I DD where U D I DD I DD I DD DI DD