3. Consider the system Y(s) W(s) = G(s) = 1 $ 1 (a) Use MATLAB command ss to calculate a state space realization (A, Bw, Cy, Dyw), Dyw (b) Now let * = Ax+Bww, y = Cyx + v, z = Cyc (c) Calculate the optimal variance of estimation error. (d) Calculate the eigenvalues of error dynamics system. (e) Calculate the transfer function T(s) from y(t) to 2(t) for your observer. (f) Calculate the poles and zeros of T(s). (g) Now, let W = 1, V = 10. Redo part (b) - (f). (h) (Bonus:) Let G(s) = Redo (a) - (f). Hint: Use question 2. = where w, v are Gaussian zero-mean white noises with covariance matrix W = 1, V = 1, respectively. Design an observer to minimize the variance of the estimation error z(t)-(t). Compute the optimal gain F. 0.