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7. matlab code: clc,clear all A=[0 1 0 0 ; 0 0 -7 0; 0 0 0 1; -53.68 0 0 0]; Q=eye(4); X=lyap(A,Q); P = X P1=det(P(1,1)) P2=det(P(1:2,1:2)) Output: P =1.0e+15 * 0.0646 -0.0000 0.0859 0.0000 -0.0000 0.6016 0.0000 3.4658 0.0859 0.0000 0.4951 0.0000 0.0000 3.4658 0.0000 4.6133 P1 = 6.4564e+13 P2 = 3.8841e+28 The beam and ball system is asymptotically stable since both p1 and p2 are positive.

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7. matlab code:clc,clear allA=[0 1 0 0 ; 0 0 -7 0; 0 0 0 1; -53.68 0 0 0];Q=eye(4);X=lyap(A,Q);P = XP1=det(P(1,1))P2=det(P(1:2,1:2))Output:P =1.0e+15 * 0.0646 -0.0000 0.0859 0.0000 -0.0000 0.6016 0.0000 3.4658 0.0859 0.0000 0.4951 0.0000 0.0000 3.4658 0.0000 4.6133P1 = 6.4564e+13P2 = 3.8841e+28The beam and ball system is asymptotically stable since both p1 and p2 are positive.


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