Polynomial matrices, division and remainder

I work in control and the following problem stumbled at me: Given to matrices N and D, obtain matrices Q and R to hold N = Q*D + R.

This solution allows to find compensator/observer pole allocation matrices.

I thank for the help.

• $Q=0$ and $R=N$ does the trick. Presumably you want to impose some additional restrictions to make it less trivial. – Eric Wofsey Jun 26 at 22:45
• Sure it holds. But assume N and D are such that $N D^{−1}$ is improper for some entries – Bruno Henrique Peixoto Jun 28 at 1:33