By Matsuda M.
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M ; n ~ Ore; Acr ¢Cmxn can be d e t e r m i n e d from Dch and the c o e f f i c i e n t s of each e n t r y of A ( k ) . A -(A ). o:j~ T . cr 1__ • , | . • . . . . =__ o:j . ^& ^ ^ ; n=n-KI-~ m . o l o . 1e) Dc Proof: Lemma 3 . 2 can be e s t a b l l s h e d by d i r e c t The q u a d r u p l e ( A c , B c , C c , ; c ) is referred oontroller) form r e a l i z a t i o n o f A-ICk). ~ B ~ verification. T:IBc, C ~ CcTc trans£ormatlen matrix, and D " so t h a t the to as a c o n t r o l l e r ,n g e n e r a l , A • (not a canonical we c ~ .
Where G V] O~lX(~p-1) 0 • I AO A -(Ao~) 1 ^ A O~xc; _~) ,' -(%pp eou . . . . P . . A . 0 o;~ 2 O~pX(Gl-l) I . 0 • • A ; " i P (3o6b) (Aog) i ~ The i t h column of A0g, i ~ l , . . , p . ~o ~ *o(°) o6o) A T. DO -~ cO; 0 ^ Eco ~ [ec01, ^ : c02 ,"- . 6e) ^ (A0,Bo,Co,D 0) is referred to as an observer (not canonical resli-atio, of A-I(x). e. 7) A-IcA) . C(kIn-A)-IB+D Theorem 3 . 2 quadruple L e t A(A) b e a r o w - r e d u c e d A - m a t r l x , (A,B,C,D). Let D~(A) b e the left which can be realized, characteristic A-matrlx using a o£ ( A , C ) .
5) A()k) - [Vh( k)-$0 (k)A0g I V0h A where D0h is the leading row matrix of A(X) and Dh(X) A diag[lV i = l , . . , m ] ; ~0(k)^ b [~01(t),~02(k) ' . . ~0p(k)lT ;^ ^~0£(k)i ~ [ 0 1 x ~ i ' l ' l ' k ' " " for ~>0~ and ~0i(k) = 01x n for ~i'0; ~i ~ j--ll ~ j , i ' l , ' " , P ; 'xVi-l'01xCn-Ti)] n ~ ~p; A0~cCnxp can be determined from Doh and the c o e f f i c i e n t s of each entry of A(X). 6a) Go(X~n-;o)-l;o+~o . where G V] O~lX(~p-1) 0 • I AO A -(Ao~) 1 ^ A O~xc; _~) ,' -(%pp eou . . . .