Find the transfer function Gs Ys=Rs for each of the

Chapter 3, Problem 14

(choose chapter or problem)

Find the transfer function G(s)=Y(s)/R(s) for each of the following systems represented in state space: [Section: 3.6]

(a) \(\begin{aligned} \dot{\mathbf{x}} & =\left[\begin{array}{rrr} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -3 & -2 & -5 \end{array}\right] \mathbf{x}+\left[\begin{array}{r} 0 \\ 0 \\ 10 \end{array}\right] r \\ y & =\left[\begin{array}{lll} 1 & 0 & 0  \end{array}\right] \mathbf{x} \end{aligned}\)

(b) \(\begin{aligned} \dot{\mathbf{x}} & =\left[\begin{array}{rrr} 2 & -3 & -8 \\   0 & 5 & 3 \\ -3 & -5 & -4 \end{array}\right] \mathbf{x}+\left[\begin{array}{l} 1 \\ 4 \\ 6 \end{array}\right] r \\ y & =\left[\begin{array}{lll} 1 & 3 & 6 \end{array}\right] \mathbf{x} \\\)

(c) \(\dot{\mathbf{x}} & =\left[\begin{array}{rrr} 3 & -5 & 2 \\ 1 & -8 & 7 \\ -3 & -6 & 2 \end{array}\right] \mathbf{x}+\left[\begin{array}{r} 5 \\ -3 \\ 2 \end{array}\right] r \\ y & =\left[\begin{array}{lll} 1 & -4 & 3 \end{array}\right] \mathbf{x} \end{aligned}\)