Chapter 4, Problem 41P

State Space SS

41. Given the following system represented in state space, solve for Y(s) using the I SS I

Laplace transform method for solution of the state equation: [Section: 4.10]

$\begin{array}{l}\text{<mover accent="true"> <mo> x </mo> <mo> ˙ </mo> </mover>}=\left[\begin{array}{ccc}0& 1& 0\\ -2& -4& 1\\ 0& 0& -6\end{array}\right]\text{x}+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]e^{-t}\\ y=\left[\begin{array}{ccc}0& 0& 1\end{array}\right]\text{x;}\text{x}\left(0\right)=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]\end{array}$