(a) Show that for the current observer specified in Section 9.5, the transfer matrix from the input \(\mathbf{U}(z)\) to the estimated states \(\mathbf{Q}(z)\) is equal to that from the input to the states \(\mathbf{X}(z)\); that is, show that \(\mathbf{Q}(z) / \mathbf{U}(z)=\mathbf{X}(z) / \mathbf{U}(z)\).

(b) Show that for the current observer specified in Section 9.5, the transfer function of the controlobserver combination of Fig. \(9-8\) is given by (9-73), which is

\[D_{c e}(z)=z \mathbf{K}[z \mathbf{I}-\mathbf{A}+\mathbf{G C A}+\mathbf{B K}-\mathbf{G C B K}]^{-1} \mathbf{G}\]

Fig 9-8

R(z)=0 | Control- estimator Dce(z) Computer U(z) (a) R(z) = 0 U(z) Dce(z) DIA Gp(s) po dana / 10 / 20 / 4 / Y(z) (b) Plant G(z) AID Y(z) Y(s)