A= [-0.4615 -2.8462 0.2308 -0.6923; 3.0769 4.3077 0.4615 2.6154; -3.3077 -5.2308 0.1538 -3.4615; -1.0000 -1.0000 -1.0000 0] A = -0.4615 -2.8462 0.2308 -0.6923 3.0769 4.3077 0.4615 2.6154 -3.3077 -5.2308 0.1538 -3.4615 -1.0000 -1.0000 -1.0000 0 B=[1 0 0 0]' B = 1 0 0 0 C=[1 0 0 1] C = 1 0 0 1 D=1; [Q,Ahat]=eig(A) Q = Columns 1 through 3 0.5590 0.5590 0.4714 -0.2236 - 0.4472i -0.2236 + 0.4472i -0.2357 0.4472 + 0.3354i 0.4472 - 0.3354i 0.7071 -0.1118 + 0.3354i -0.1118 - 0.3354i -0.4714 Column 4 -0.5774 -0.0000 0.5774 0.5774 Ahat = Columns 1 through 3 1.0000 + 2.0000i 0 0 0 1.0000 - 2.0000i 0 0 0 2.0000 0 0 0 Column 4 0 0 0 0.0000 Qm=[real(Q(:,1)) imag(Q(:,1)) Q(:,3) Q(:,4)] Qm = 0.5590 0 0.4714 -0.5774 -0.2236 -0.4472 -0.2357 -0.0000 0.4472 0.3354 0.7071 0.5774 -0.1118 0.3354 -0.4714 0.5774 re=real(Ahat(1,1)); im=imag(Ahat(1,1)); Am=Ahat; Am(1,1)=re; Am(2,2)=re; Am(1,2)=im; Am(2,1)=-im; Am Am = 1.0000 2.0000 0 0 -2.0000 1.0000 0 0 0 0 2.0000 0 0 0 0 0.0000 Bm=inv(Qm)*B Bm = 2.7521 -0.6880 -1.3055 -0.1332 Cm=C*Qm Cm = 0.4472 0.3354 0.0000 -0.0000 Dm=D Dm = 1 sys=ss(A,B,C,D); tf(sys) Transfer function: s^4 - 3 s^3 + 3.539 s^2 - 3.077 s + 2.401e-016 ---------------------------------------------- s^4 - 4 s^3 + 9 s^2 - 10 s + 8.468e-016 sysmodal=ss(Am,Bm,Cm,Dm); tf(sysmodal) Transfer function: s^4 - 3 s^3 + 3.539 s^2 - 3.077 s - 4.791e-016 ---------------------------------------------- s^4 - 4 s^3 + 9 s^2 - 10 s + 8.468e-016 exit