Page 1 .... Page 2 ..... 2a PaGT : (50). Then ( ~A +1~A; ~E) is detectable for all 1A 2 U if and only if. ~A +1~A is asymptotically stable for all 1A 2 U. In this case,.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 42, NO. 2, FEBRUARY 1997
ACKNOWLEDGMENT The authors gratefully acknowledge the comments and suggestions of the two anonymous referees as well as the fruitful discussions with S. Shahriari. They would also like to thank T. Ando for pointing out an error in the original version of the manuscript.
. Although we do not require that V11 and V21 be equal to V1 and V2 , respectively, 2 V2 , where the we shall require for technical reasons that V21 nonnegative scalar is a design variable. Before continuing it is useful to note that for a given compensator A is asymptotically stable for all A 2 U , Ac ; Bc ; Cc , if A then the performance (7) is given by
J (Ac ; Bc ; Cc ) = where
1 V1 V~ =
tr P1A~ V
Bc V2 BcT