eigen value of the transfer function 2x2 matrix
60 views (last 30 days)
Show older comments
hello
I have 2x2 matrix
G=[1/(s+1) 1/(s+2);1/(s+3) 1/(s+4)] where G(1,1)=/(s+1) G(1,2)=1/(s+2) G(2,1)=1/(s+3) G(2,2)=1/(s+4)
Now because it is a 2x2 matrix it must have 2 eigen values .
so my questions are:
- How to calculate the determinant of G matrix?
- How to find the eigen values of the G matrix?
- How to get the eigen vectors of the G matrix?
- I want to perform the following operation ------- SQUAREROOT OF((G(1,1)+G(2,2))/2) but I am unable to do.
1 Comment
Paul
on 25 Aug 2020
Edited: Paul
on 25 Aug 2020
The discussion below indicates these questions are related to multivariable stability analysis. But it's not clear how any of your questions 3-4 actually relate to that type of analysis. Can you clarify what you're actually trying to do and explain why you need to complete the operations in questions 3-4?
Accepted Answer
Paul
on 26 Aug 2020
Edited: Walter Roberson
on 26 Aug 2020
If you want to use the symbolic appoach, why not just create a matlab function to evaluate lambda(2) and then create the plot using an frd model:
syms s
G=[1/(s+1) 1/(s+2);1/(s+3) 1/(s+4)];
lambda=eig(G);
f=matlabFunction(lambda(2));
w=logspace(-1,3,500);
nyquist(frd(f(1j*w),w));
Unclear how well this symbolic approach will work for systems of even moderate complexity ....
2 Comments
Paul
on 26 Aug 2020
Walter,
I see that you edited my answer, I think to remove the >> from the code snippet. Can anyone edit anyone else's Answer?
Walter Roberson
on 26 Aug 2020
You are correct, I removed the >> so that the code could be copied and pasted.
People with reputation 3000 or higher can edit answers. That is about 45 people (out of over 200000 users) . We mostly reformat text into code, or adjust html links to be usable, but sometimes we remove >> so that code can be run more easily. Sometimes we fix spelling mistakes that are interfering with understanding what has been posted (a lot of the users do not have English as a first language, so incorrect spelling can make it difficult for them to understand what was said.)
Less pleasantly, from time to time we remove inappropriate wording such as personal insults.
More Answers (3)
Walter Roberson
on 23 Aug 2020
If you use the symbolic toolbox,
syms s
G=[1/(s+1) 1/(s+2);1/(s+3) 1/(s+4)]
then you can do all of those operations directly.
If you use
s = tf('s');
G=[1/(s+1) 1/(s+2);1/(s+3) 1/(s+4)]
then you can do det(G) and eig(G) but eig(G) will not return the eigenvectors
An example of finding eigenvectors from eigenvalues is at https://www.scss.tcd.ie/Rozenn.Dahyot/CS1BA1/SolutionEigen.pdf
SQUAREROOT OF((G(1,1)+G(2,2))/2)
The sqrt() is the problem; sqrt() is not defined for transfer functions
Maple tells me that that particular expression might have an inverse laplace,
exp(-4*t)*int(3*((4*Dirac(_U1)*sqrt(t - _U1))/3 + sqrt(t)*exp((9*_U1)/4)*(BesselI(0, (3*_U1)/4) + BesselI(1, (3*_U1)/4)))/sqrt(t - _U1), _U1 = 0 .. t)/(4*sqrt(Pi)*sqrt(t))
0 Comments
MANAS MISHRA
on 28 Aug 2020
Edited: Walter Roberson
on 28 Aug 2020
2 Comments
Paul
on 28 Aug 2020
Edited: Paul
on 28 Aug 2020
Obviously I don't know what you're actually trying to accomplish, but I really doubt you need to use a 50000 pont vector spanning the entire space of usable frequencies. But maybe you do. Along those same lines, is computing the eigenvalues symbolically going to work for problems of even moderate complexity? I have basically no experience with the Symbolic Toolbox and don't really know what its limitations are in computing eigenvalues symbolically. And even if you can get expressions for the eigenvalues, they may very well be very high order polynomials that may not lend themselves well to numericaly evaluation.
See Also
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!