Problem 1 (30 Points): Highlight Your Final Answers The state space model of a system is given by 1 2001?X1 where x1 and x2 are the state variables, u is the input and y is the output (all scalars). a. b. c. Write down the A, B, C, D matrices What are the system poles? Compute by MATLAB Write down the matrix formula for the Laplace transform of the output Y (s) in terms of the Laplace transform of the input U(s) with state vector initial conditions Xo What is the formula for the transfer function matrix? d. e. Given the three state variables initial conditions are x1 (0) - 0, x2(0) 0, x3 (0) 1, expand and simplify the expression in part (c) to the following form: Y(s) = G(s)U(s) + 1(s) where G (s) is the system transfer function and I(s) is due to initial conditions x,o f. Find system time response y(t) when system input u is a step function of magnitude 3. g. Convert the above continuous time system into a discrete time system given sampling period T- 0.1 seconds. Use MATLAB "ss" and "c2d" commands, clearly write down or highlight the discrete time A,B,C,D matrices