1. Consider the discrete Gauss-Markov Random Process [x(k+)] = [0:2 0.][**)]+[j]w(k) where the output is y(k)=...

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1. Consider the discrete Gauss-Markov Random Process [x(k+)] = [0:2 0.][**)]+[j]w(k) where the output is y(k)= x(k) and w is a zero-mean, purely-random Gaussian sequence with variance W. Solve the discrete Lyapunov equation for the steady-state covariance matrix X, and find the steady-state variance of the output, E(y2), in terms of W. Verify your result using the Matlab dlyap function. 1. Consider the discrete Gauss-Markov Random Process [x(k+)] = [0:2 0.][**)]+[j]w(k) where the output is y(k)= x(k) and w is a zero-mean, purely-random Gaussian sequence with variance W. Solve the discrete Lyapunov equation for the steady-state covariance matrix X, and find the steady-state variance of the output, E(y2), in terms of W. Verify your result using the Matlab dlyap function.