Chapter 4, Problem 42P

State Space SS

42. Solve the following state equation and output equation for y(t), where u(t) is the unit step. Use the Laplace transform method. [Section: 4.10]

$\begin{array}{l}\text{<mover accent="true"> <mo> x </mo> <mo> ˙ </mo> </mover>}=\left[\begin{array}{cc}-3& 0\\ -1& -1\end{array}\right]\text{x}+\left[\begin{array}{c}2\\ 1\end{array}\right]u\left(t\right)\\ y=\left[\begin{array}{cc}1& 0\end{array}\right]\text{x;}\text{x}\left(0\right)=\left[\begin{array}{c}2\\ 0\end{array}\right]\end{array}$