Observability and controllability properties depend on the state-space representation chosen for a given system. In general, observability and controllability are affected when pole-zero cancellations are present in the transfer function. Consider the following two systems with representations:

a. Show that both systems have the same transfer function G_i(s) = Y(s)/ R(s) after pole-zero cancellations.

b. Evaluate the observability of both systems.

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ši = A,x; = B;r y = C;x;; 1 A1 B1 ; C = [2 0] -2 -3 1 A2 = 1; B2 = 0|; C2 = [6 2 0 -6 -11 -6