Assume the following state space representation of a discrete-time servomotor system. (as a review for the final exam, you might check this state space representation with the difference equation in problem 1 on homework 2. this parenthetical comment is not a required part for homework 8.) 1.9048 x(n) +lo.04679 0.04679/(n) compute the open-loop eigenvalues of the system. that is, find the eigenvalues of ф. check controllability of the system. or, answer the question: is it possible to move the open-loop eigenvalues to arbitrary new values using full-state feedback? using full-state feedback, u(n) - -kx (n), find the full-state feedback gain matrix, k, to locate the closed-loop eigenvalues (eigenvalues of фе-ф-гк) at z i. a. b. c. j * -0.8 incorporate a reference input with full-state feedback into the system from problem 2. that is, let the input be u(n) - -kx(n) + n1r(n). use the full-state feedback gain matrix found in problem 2. a. find the value of n that will produce a dc gain from the reference input to the output of 1.0 use matlab to plot the step response for this closed-loop system using the value of n1 from problem 3.a. b. c. use matlab to plot the step response for this closed-loop system with n d. compare the step responses from problem 3.b. and problem 3.c. 1