Computing the inverse of polynomial matrices

Question

Raphaël 2013-4-30

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https://ww2.mathworks.cn/matlabcentral/answers/74095-computing-the-inverse-of-polynomial-matrices

Dear all,

Considering a polynomial matrix of the form

A(z)=z^n*A_n + z^{n-1}*A_{n-1}+...+z*A_1+A_0 where the A_i are real _square_ matrices,

Are there Matlab functions designed to compute the inverse of such a polynomial matrix ?

Any advice or comment is welcome,

Thank you,

Raphaël

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Matt J 2013-4-30

编辑：Matt J 2013-4-30

Do you mean you want a symbolic inverse?

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Answer 1

K1 2013-9-6

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I have noticed that you cannot easily calculate the inverse (symbolic or not). I just read a paper describing an algorithm on how to do the inverse and get an expression of the inverse as based on A_i.

In scilab there is function doing this (calculating coefficients) and if you have POLYX software (which is not free), you will be able to do it as well in MATLAB. I haven't come up with a solution yet. But I think I have to implement the algorithm myself.

Cheers Keivan