3. Consider the discrete-time state-space equation x (k+1) = 1 1 1x (k) + u (k)...

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3. Consider the discrete-time state-space equation x (k+1) = 1 1 1x (k) + u (k) 0 1 y(k) = [200] (k) Find the state feedback gain so that the resulting feedback system has all eigenvalues at z = 0. Show that for any initial state, the zero-input response of the feedback system becomes identically zero for k > 3. 3. Consider the discrete-time state-space equation x (k+1) = 1 1 1x (k) + u (k) 0 1 y(k) = [200] (k) Find the state feedback gain so that the resulting feedback system has all eigenvalues at z = 0. Show that for any initial state, the zero-input response of the feedback system becomes identically zero for k > 3.