294 CON TROLLER RED UCTION art of Prolilem-=-is satis/ed by a controller K,Hence to reduce the order of the cntroller KEit is sufficient to solve a frequency weighted model reduction roblem if W can be calculated,In the single in ut and single out ut caseEa "smallestoweighting function WS)can be calculated using the art of Prollem-=-as follows IW4w川6spFu4Tm4w),·p儿 Re eated Problem-=-and Problem-)using the above method,(Hint"W can be com uted frequency ly frequency using u software and then Atted by a stable and minimum Vhase transfer function,1 Problem -,2 One way to generalize the method in Prollem-==to MIMO case is to tae a diagonal W W=diag4W,Wr,Wm） and let Wi be com uted from IW4w)川6sup |eFum4w),·p)引 )s where e is the i th unit vector. Nert tet a)be com uted from 1 a4iw)6 sup |W-1FuT雪w),·p)川 71 P)S where W=diag④V,W, ,...Wm),Then a sutable W can be tallen as W=aW. A ly this method to Problem-3, Problem -fi Generalize the rocedures in Problem-==and Problem-=6 to rob" lems with additional structured uhcertainty cases,(A more general case can be fourd in Yang and Pacard 9fff-il,￾ CONTROLLER REDUCTION part  of Problem  is satised by a control ler K Hence to reduce the order of the control ler K it is su cient to solve a frequency weighted model reduction problem if W can be calculated In the single input and single output case a smal lest weighting function Ws can be calculated using the part  of Problem  as fol lows jWjj  sup P  jFuTzw j pj Repeated Problem  and Problem  using the above method Hint W can be com puted frequency by frequency using software and then tted by a stable and minimum phase transfer function Problem  One way to generalize the method in Problem  to MIMO case is to take a diagonal W W  diagW WWm and let W i be computed from jW ijj  sup P  je T i FuTzw j pj where ei is the i th unit vector Next let s be computed from jjj  sup P  jW FuTzw j pj where W  diagW W  W m Then a suitable W can be taken as W  W  Apply this method to Problem  Problem  Generalize the procedures in Problem  and Problem  to prob lems with additional structured uncertainty cases A more general case can be found in Yang and Packard