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= (State equations for interconnections of linear systems) Let Hi(s), i 1, 2, be two transfer function matrices with state-space realizations (A, B, C,


   

  

= (State equations for interconnections of linear systems) Let Hi(s), i 1, 2, be two transfer function matrices with state-space realizations (A, B, C, Di), i = 1,2, respectively. Suppose the dimensions of H(s) are such that all the expressions in the following are well defined. U B D S A x1 C B2 D2 S A2 X2 C Negative feedback: Draw a block diagram of the system with transfer function Hfeedback = H1(s)(I + H(s)H(s))-, which consists of the negative feedback connection of the two subsystems, with H(s) in the feed forward path, and H(s) in the feedback path. Find a state-space realization (A, B, C, D) for H(s).

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