For the linear system x=Ax+Bu y = Cx+Du,

[

0 0 -1] A= 1 0-3 , 0 1 -3

[0 1 OJ C= 001 ' D=[O].

(a) Design a full-order state estimator for the system.

(b) Find an optimal control that minimizes the cost function where [
3 0 0] R =I, Q = 0 2 0 0 0 1 Problem