Multivariable Zeros using Generalised Eigenvalue Problem

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Akshay Vivek Panchwagh
评论： Akshay Vivek Panchwagh 2022-7-27
So I have the following matrices which represent a state-space configuration:
A = [-3 5 -7 0; 0.5 -1.5 0.5 -7.5; -5 0 -3 0; -0.5 -5 0 -7];
B = [1 0; 0 -1; -2 0; 0 1];
C = [1 0 0 0; 0 -1 0 0];
D = [-1 0; 2 0];
As mentioned in the question, I need to find the multivariable zeros of the above system using generalised eigenvalue problem.
I understand that ideally, generealised Eigenvalues can be obtained from
[V,D] = eig(A,B)
However, if I try to input my matrices in this code, it does not run for the obvious reasons. I tried doing
[V,D] = eig(A,A)
and it works, but I am not sure if that is the right way. Even so, I am unable to figure out how I can calculate zeros from the V and D matrices.
Can anyone please suggest me how I can approach this problem at hand?

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回答（1 个）

Paul
Paul 2022-7-26
Is tzero what you're looking for?
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Paul
Paul 2022-7-27
If using the definitions on the doc page tzero, the invariant zeros are the same as the transmission zeros when the realization is minimal. minreal to find the minimal realization, and then tzero() on the result. At least I think that's how it's supposed to work.
Akshay Vivek Panchwagh
Akshay Vivek Panchwagh 2022-7-27
The system I have is already in a minimal realisation. So, I believe the zeros I'll get by using tzero are indeed the transmission zeros. The task further mentions about simulating the system response but I think thats another question in itself. Thank you nevertheless.

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