Xdentifiability of Closed Loop Systems Using the Joint Input-output

. . . . , ' Abst rac t . The i d e n t i f i a b i l i t y o f m u l t i p l e i n p u t m u l t i p l e ou tpu t l i n e a r dynamic . . . . . . . systems opera t ing i n closed loop is considered f o r t h e 'case where t h e p l a n t . . and t h e r e g u l a t o r dynamics a r e both l i n e a r and t ime-invariant . T w o b a s i c iden: t i f i c a t i o n methods h a v e b e e n proposed f o r such systems : t h e j o i n t input-outpu t method. i n which t h e i n p u t and ou tpu t processes a r e modeled j o i n t l y a s t h e ou tpu t of a white n o i s e d r iven system r a n d t h e d i r e c t method, i n which a pre. . d i c t i o n e r r o r method is used on t h e input-output d a t a j u s t a s if t h e iystem . . . . ' were i n open loop. Prev iqus ly ob ta ined i d e n t i f i a b i l i t y r e s u l t s f o r t h e jo i r i t inpu t -ou tpu t method a r e extended t o a v a r i e t y o f new s i t u a t i o n s , inc lud ing . a . . : p o s s i b l e one-sided c o r r e l a t i o n between t h e r e g u l a t o r no ise and t h e process noise. These new i d e n t i f i a b i l i t y condi t ions a r e now very c l o s e t o t h o s e ob ta i6. , . ed. f o r t h e d i r e c t method. . . . . . . . . . .