Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement

Question

I wish to find the polynomials B(s) and A(s) in the following compensator equation:

A(s)D(s) + B(s)N(s) = F(s)

Given,

$$N(s) = s - 2$$

$$D(s) = s^2 - 1$$

$$F(s) = s^2 + 3*s + 4$$

Condition

The degree of B(s) should be less than the degree of A(s)

Answer 1

your question is ill-conditioned: If $A$ must have a higher degree than $B$, 2 things can happen: $A$ is a constant, meaning $B$ must be 0: which means you cannot solve the equation as there is no $s$ term in $A(s)(s^2-1)$. Or $A$ is of order one (atleast one $s$) and $B$ is a constant: Which means the function can not be solved as there will be a $s^3$ present on the left hand side.

Therefore, I am certain you made a mistake somewhere