6%y Robust Stabilization of Coprime Factors 297 Figure 16.2:LFT Diagram for Coprime Factor Stabilization and Uis a unitary matrix.Let r=(1+DD)5衣Z Then Tllo =U*Tllo =Twllo and the problem becomes one of finding a controller K so that lo 5.with the following generalized plant 0 (I+DD) A -LZ1- 0 (I+D*D)D*ZI- I ZC I ZD(I+D*D) Now the formulae in Chapter 14 can be applied to G to obtain a controller K and then the K can be obtained from K=-(I+D*D)1KZ.We shall leave the detail to the reader.In the sequel,we shall consider the case D=0 and Z=I.In this case,we have 1 and Xo4-)+(4-9rx-Xan-x。+C-0 Yo(4+LC)*+(4+LC)Yo -Yo C*CYo =0. Robust Stabilization of Coprime Factors ￾ M i K ￾ ￾ N ￾  ￾ ￾ y u z z w Figure ￾ LFT Diagram for Coprime Factor Stabilization and U is a unitary matrix Let K  I  DD ￾ KZ ￾ z z  U ￾ z z  Then kTzwk￾  kUTzwk￾  kTzw k￾ and the problem becomes one of nding a controller K so that kTzw k￾  with the following generalized plant G  ￾ U   Z G ￾ I   I  DD ￾        A LZ B ￾ I  DD  ￾ C I  DD ￾ DC ￾ I  DD  ￾ Z I  DD ￾ DZ ￾  I ZC I ZDI  DD ￾       Now the formulae in Chapter  can be applied to G to obtain a controller K and then the K can be obtained from K  I  DD ￾ KZ  We shall leave the detail to the reader In the sequel we shall consider the case D   and Z  I  In this case we have   and X￾A  LC    A  LC    X￾  X￾BB  LL    X￾  CC      Y￾A  LC  A  LCY￾  Y￾CCY￾