Consider the following third order system: The output of the system is given as x = y 2 - $3 X = -2z+u y = -f w(t) = x a) Find the relative degree of the output and show that the system is fully feedback linearizable. b) Construct the control signal u such that the nonlinear terms are eliminated. c) Indicate the coordinate transformation T = (x, y, z) and write down the state space model in the new coordinates (You can use the letter q | i = 1,2,3 for the new coordinates). d) Construct the input (v) for the linearized system such that the reference tracking error (e = x - xref) approaches to zero.