Solving for an unkown matrix

Is there a way to solve the following matrix equation in matlab?

P*A + B*P = C

A,B,C,P have the same matrix dimensions. A,B,C are known matrices. P is an unknown matrix.

Answer 1

[Teja Muppirala]

This is the Sylvester equation. You can solve it using the LYAP command.

A = rand(3);
B = rand(3);
C = rand(3);
P = lyap(B,A,-C)

P*A+B*P - C

Answer 2

[Walter Roberson]

Computationally, it can be solved when A, B, and C are given -- with, of course, exceptions for cases such as A and B are all 0 and C is not.

However, I do not know if there is a good way to formulate what the solution will be. I have the general symbolic 4 x 4 case running now, and it is taking its sweet time...