Solving unknwon matrix in a matrix equation using symbolic and kronecker

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Hi, I need some help on how to solve the matrix equation below in MATLAB. I tried doing it using the symbolic toolbox and kronecker function but I am not able to obtain the final P matrix shown below. I wonder if MATHCAD is my best option to solve it. Any help is appreciated.
Here are the different matrices. L is a matrix as well. wp, wc and wv are constants.
Here is the resulting P matrix I need to get.
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mpz
mpz 2023-5-17
@Torsten I am trying to know how to derive this one because I have a similar problem and I would like to know how this one was derived. Trying to not have to do it analytically.

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