Riccati matrix P

In general, for a second-order system, when Q is a diagonal matrix and R is a scalar quantity, the elements of the Riccati matrix P are... 

In reverse-time, starting with P(A ) = 0 at NT = 20 seconds, compute the state feedback gain matrix K(kT) and Riccati matrix P(kT) using equations (9.29) and (9.30). Aiso in reverse time, use the desired state vector r(/c7 ) to drive the tracking equation (9.53) with the boundary condition s(N) = 0 and hence compute the command vector y kT). 

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 ... 

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