Consider the system of Problem 8.10, given by (a) Find the system output for u(...

Consider the system of Problem 8.10, given by

(a) Find the system output for u(t) = 0 and the initial states given by x(0) = [1 0]^T.

(b) Find the unit step response of the system, with x(0) = 0, using (8.28) and y(t) = Cx(t) + Du(t).

(c) Verify the results in part (b), using the system transfer function and the Laplace transform.

(d) Use the transfer function to write the system differential equation.

(e) Verify the results of part (b), by substituting the solution into the system differential equation.

(f) Find the system response with the initial conditions of part (a) and the input of part (b). Verify that the response has the correct initial condition.

(g) Use SIMULINK to verify the results of part (f).