Problem 9.6-7 is to be repeated for the current observer, with the mode of $Q\left(z\right)$ equal to $(A-GCA{)}^k$.

Problem 9.6-7

For the system of Problem 9.6-5, use a transfer function approach to show that the transfer function Q(z)/U(z) is first order (even though the system is second order) and is equal to X(z)/U(z). Hence the mode of Q(z), which is (A - GC)k, is not excited by the input signal u(k).