For the given system, find the full-state feedback gain matrix, k, to place the closed-loop poles at z0.9 1j0.1. x(n + 1) = φχ(n) +「u (n), with 0.5 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.) 2. 0.048371 u(n) 1 -.9048 o/r(n) + r(n + 1)- [1.9048 y(n) = [1,0]x(n) compute the open-loop eigenvalues of the system. that is, find the eigenvalues of φ 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), find the full-state feedback gain matrix, k, to locate the closed-loop eigenvalues (eigenvalues of φ e-φ-tk) at za-0.8 0.2. a. b. c. j * 3. 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. find the value of ni that will produce a dc gain from the reference input to the output of 1.0. a. b. use matlab to plot the step response for this closed-loop system using the value of n from problem 3.a c. use matlab to plot the step response for this closed-loop system with m 1 d. compare the step responses from problem 3.b. and problem 3.c.