I have a characteristic equation that yields
s^3+as^2+s+b=0
I am supposed to determine the areas in ab-plane that correspond to a stabile system, I just dont know how to begin with, is it Ruth Hurwitz Iam supposed to use?, any hint is welcome

 

You can certainly use Routh-Hurwitz criterion. Presumably you are considering a linear time-invariant system.

For your case

\(s^3+as^2+s+b=0\)

Two conditions must be met

1. the coefficients of all terms on the LHS of the equation must be greater than zero. So in particular a and b must be greater than zero.
2. a>b