The state space model of a system is given by: \frac{d}{d t}\left[\begin{array}{l}

x_{1} \\

x_{2}

\end{array}\right]=\left[\begin{array}{cc}

-1 & 0 \\

1 & -2

\end{array}\right]\left[\begin{array}{l}

x_{1} \\

x_{2}

\end{array}\right]+\left[\begin{array}{l}

2 \\

1

\end{array}\right] u ; \quad y=\left[\begin{array}{ll}

2 & 1

\end{array}\right]\left[\begin{array}{l}

x_{1} \\

x_{2}

\end{array}\right] Where: x₁ and x₂ are the state variables, u is the input and y is the output (all scalars). Write down the A, B, C, D matrices. Find the system poles. Is system stable? Explain why or why not. What is the Laplace transform of the output Y(s) in terms of the Laplace transform of the input U(s) with initial condition x = [9]? (Use eq. 7-6 Handout 7.) Expand and simplify your answer to the following form by MATLAB symbolic: e. What is G(s) called? Y(s)=G(s) U(s)+I(s) What is I(s) due to? Find the system response y(t) given u is a unit step input: U(s) = = 1/s. Now, plot the response y(t) using MATLAB fplot command for 0 < t < 10. Plot the response of part (g) using MATLAB control system toolbox commands. Define A,B,C,Dmatrices in MATLAB then use below commands that will plot the unit step response for 10 seconds;Compare to the plot of part (h); they must be identical: