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By Charters Samuel

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10) the two 0-polynomial matr i c es on the left h an d side are n-unimodular. Thus Af [ [ B1 [ P2 = (3. 12) Ia O ] 0 14 A l P1 - A 3 B3 and i t ] o] follows immediately that [ B1 Al to be N(s) --? 3 (3. 13) Pi 0 0 P1 (s) ] (3. e. and so P1 ( s ) , F2 ( s) or equivalently P1 (s) , h ave the same zero structure and rank defect n. 0 are P2 (s) ( 3. 3) P2] : = vn(P2) (Af (s) P2 (s )] a n d [fai (s)T - N(s)T]T have ful l \/so E n. ial matrices A1{s), A2(s) , B1 (s) , B2(s) such ( 3. 4) D i'" l (s) rank If 0 P1 (s), P2(s) E P(p, m) _ -N(s) where Equivalence of Mah-ices in n � C U { oo } .

Where (6) s e l ected h e r e W i t h the Ka l m a n g a i n 1 s t a t e - s p a c e d e s c r ipt i o n d i me n s i o n I n f a ct 1987 ; l i n e a r e s t imator 0 en - a n ach ieve o p t i ma l i t y , 0 (n + k) which w i l l be conditio ns . 0 1 -a 1 0 R zero . re­ (5) further here where K i s t h e bo Q 0 which x(t) b e in g f e d b ac k ( fi = actual c o n s idered vector with this x ( t + l ) = Px ( t ) +Qu ( t ) +K [ y ( t ) - Hx ( t } ) 0 wh e r e a s con­ x(t} ? in which F t he n when In the state s t r u c t e d to p r o v ide x ( t ) .

5) and the following H00 requirement on the transfer function matrices T;(s) viewed from the exogenous input W; and the selected output Yi : (3. 1 ) where O; (i = 1 ,m) arc specified weighting factors. Using corollary 2 . 1 we get tl�c following lemma : Lemma 3 . 1 - For a given control law u sat is fyi ng ( 1 . 5) is quadratically stable and t he l f00 requirements (3. 5 auxiliary system is quadratically stable with the same control law. ; II ::; o; (for i=l ,m) @ The H00 requirements (3. 2). 3) the function T\(X) is also multiplied b y the same factor which indicates that T\(X) may be viewed as a sensitivity function of the closed loop system with respect to the specified uncertainties and attenuation requirements.

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