gramian singular value decomposition

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Jack
Jack 2013-3-25
I would like to measure the effect of certain modes in a state space model. I am using singular value decomposition of the controllability and observability gramians to identify which modes are dominant. For example, I have a 4 state system:
A = [-1.6,1,-1.1811,-0.1181;2,-2.446,-1.813,1.1805;0,0,0,1;-7.196,-0.445,-56.82,-5.53];
B = [-0.07,-0.006;3.726,-0.28;0,0;0.572,0.019];
C = [0,1,0,0;-32.65,-28.04,49.93,2.37;-11.69,-35.68,65.02,6.27;3.68,-38.040,153.63,17.68];
D = [0,0;-1.02,-12.55;0,-1.23;-1.2,3.69];
sys = ss(A,B,C,D);
Wc = gram(sys,'c');
[U,S,V] = svd(Wc);
I know svd ranks its output in descending order, so how would I be able to trace which output relates to which mode? Eventually, I would like to use this on much larger systems.
Thanks,
Jack

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