Use MATLAB to find the transfer function, G(s)=Y(s)/R(s),

Chapter 3, Problem 15

(choose chapter or problem)

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

(a) \(\dot{\mathbf{x}}=\left[\begin{array}{rrrr}0 & 1 & 5 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ -7 & -9 & -2 & -3\end{array}\right] \mathbf{x}+\left[\begin{array}{l}0 \\ 5 \\ 8 \\ 2\end{array}\right] r\)

\(y=\left[\begin{array}{llll} 1 & 3 & 6 & 6 \end{array}\right] \mathbf{x}\)

(b) \(\begin{aligned} & \dot{\mathbf{x}}=\left[\begin{array}{rrrrr} 3 & 1 & 0 & 4 & -2 \\ -3 & 5 & -5 & 2 & -1 \\ 0 & 1 & -1 & 2 & 8 \\ -7 & 6 & -3 & -4 & 0 \\ -6 & 0 & 4 & -3 & 1 \end{array}\right] \mathbf{x}+\left[\begin{array}{l} 2 \\ 7 \\ 8 \\ 5 \\ 4 \end{array}\right] r \\ & y=\left[\begin{array}{lllll} 1 & -2 & -9 & 7 & 6 \end{array}\right] \mathbf{x} \end{aligned}\)