How to solve matrix function in Matlab?

Hi all! I'm faced with the following question:

X=AXB+C

where A is a 4*4 matrix, B is a 3*3 matrix, X and C are 4*3 matrices. I know the values of A, B and C. How can I solve out X using matlab?

[Qiaohairuo Lin]

Thank you so much, Hoffrichter and Star Strider. I found out that there is a function called sylvester which can directly address the question.

[Star Strider]

I considered that, however it does not appear to be a Sylvester system, at least as I interpret it. Another option I considered was lyap and its friends.

[John D'Errico]

inv(A)*X + X*(-B) = inv(A)*C

help sylvester

 SYLVESTER Solve Sylvester Equation.
    X = SYLVESTER(A,B,C) solves the Sylvester equation A*X + X*B = C,
    where A is a m-by-m matrix, B is a n-by-n matrix, and X and C are
    m-by-n matrices.

    Documentation for sylvester
       doc sylvester

Answer 1

[Paul Hoffrichter]

Define Z = AXB + C - X

You have to start off with your initial best guess for X based upon the nature of the model. For lack of any information, guess that X_0 = C. (Then Z = ACB.)

Create a Q = cost function for Z. You could try the trace of Z, and then check to see if Z has all entries close to 0.

https://www.mathworks.com/help/matlab/ref/double.trace.html

You then need to find a zero crossing of your cost function. To do this, you can use fzero.

https://www.mathworks.com/help/matlab/ref/fzero.html

Other initial guesses may result in different answers if there are multiple roots.