For an i show that if pnn converges to a steady state

Question

In many cases, the error covariance matrix P(nln) will converge to a steady-state value Pas n → ∞. Assume that C, Q_w, and Q_v are the limiting values of C(n), Q_w(n), and Q_v(n), respectively.

(a) For A(n) = I, show that if P(n|n) converges to a steady state value P, then the limiting value satisfies the algebraic Ricatti equation PC^H(CPC^H + Qv)^-1 P- Q_w = 0

(b) Derive the Ricatti equation for a general state transition matrix A(n) that has a limiting value of A.