The plant described in Example 9.8 by equations (9.185) and (9.186) is to be controlled by a Linear Quadratic Gaussian (LQG) control scheme that consists of a LQ Regulator combined with the Kalman filter designed in Example 9.8. The quadratic performance index to be minimized for the LQ regulator is of the form given in equation (9.181) where Q=1000050001(R=1) Using the recursive equations (9.29) and (9.30), solve, in reverse time, the Riccati equation commencing with P(N)=0. If the sampling time is 0.1 seconds, the values of the discrete-time state transition and control matrices A(T) and B(T) calculated in Example 9.8 may be used in the recursive solution. Continue the recursive steps until the solution settles down (when k=50, or kT=5 seconds) and hence determine the steady-state value of the feedback matrix K(0) and Riccati matrix P(0). What are the closed-loop eigenvalues? Solutions K(0)=[0.1060.5810.064]P(0)=11.4743.4060.1533.4063.9520.1630.1530.1630.1086 closed-loop eigenvalues =1.230 4.816j2.974