How do I find the the zero state direction and the zero input direction of a transfer matrix in Matlab?
I want to compute using matlab the Rosenbrock System Matrix, and in particular I am trying to do a an analysis similar to the one at the end of http://people.duke.edu/~hpgavin/ce263/zeros.pdf . So, starting from a transfer matrix I would like to show that if there is a zero at a certain position, there is a zero blocking property. To do so, as written in the link, I have to find the zeros state direction and the zero input direction, and I am having troubles doing do. I am considering a different system from the one in the link, so I am trying to do a similar analysis applied to another system, and I am doing this: s = tf('s'); P = 1/(s+5); C = 6/s; S = 1/(1+P*C); T = P*C/(1+P*C); G_2 = [T S; S -S]; %transfer matrix Now, I have that my transfer matrix is : G_2 and for it I would like to do the analysis to find the zero state diretion and the zero input direction, but I am having troubles doing so. Can somebody please help me? Thanks in advance.
John Michell answered .
2025-11-20
To reproduce that analysis:
s = tf('s');
P = [2/(s^2+3*s+2) 2*s/(s^2+3*s+2); -2*s/(s^2+3*s+2) -2/(s^2+3*s+2)]
S = ss(P)
Smr = minreal(S)
A = Smr.A
B = Smr.B
C = Smr.C
D = Smr.D
trz = tzero(A,B,C,D)
RSM_1 = [eye(3)-A B; -C D]
rRSM_1 = rank(RSM_1)