Consider a dynamic system whose state-variable matrix equations are expressed as follows:

The matrices \(\mathbf{A}, \mathbf{B}, \mathbf{C}\), and \(\mathbf{D}\) are given by 

(a) Use MATLAB to find the transfer function of the system.

(b) Draw the system block diagram, indicating the matrices \(\mathbf{A}, \mathbf{B}, \mathbf{C}\), and \(\mathbf{D}\), the vectors \(\dot{\mathbf{x}}\) and \(\mathbf{x}\), and the variables \(r(t), u(t)\) and \(y(t)\).

(c) Compare the root locus obtained by using the State-Variable Matrix model and that obtained using the transfer function form.

x=Ax+Bu y=Cx+Du u=r-y.