Problem 4 (20 points) Consider following discrete time system x(k+1)=( s )x(k) + (7) u(k), y(k) = (3 0) (k). = -1.5 It i

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Problem 4 20 Points Consider Following Discrete Time System X K 1 S X K 7 U K Y K 3 0 K 1 5 It I 1 (60.82 KiB) Viewed 57 times

Problem 4 (20 points) Consider following discrete time system x(k+1)=( s )x(k) + (7) u(k), y(k) = (3 0) (k). = -1.5 It is desired to place the closed loop poles at 21 = -0.5 and 22 = -0.8 by using a state feedback control u(k) = -Kî (k) where î (k) is the observed state. The observer gain matrix should be chosen such that the observer poles are at 201 0.3 and 802 0.3. Determine the control gain K and the observer gain matrix. Present the obtained observer equation. =