Consider the plant of Example 9.2, which is (a) Is this system observable? (b) Explain the reason

Question:

Consider the plant of Example 9.2, which is x(k + 1) = Suppose that the output is given by 1 0.0952 0.00484 0.9048] 0.0952|u(k) x(k) + y(k) = [0 1]x(k)

(a) Is this system observable?
(b) Explain the reason for your answer in part (a) in terms of the physical aspects of the system.

Example 9.2 We will solve the design in Example 9.1 via Ackermann's formula (9-25). The plant model is given by and the 0.0048374 0.095163 Then the gain matrix is, from (9-25), K = [0 1] [B AB] = -95.082 105.082 0.0138934