ROUTH–HURWITZ CRITERION
The stability of a sampled data system can be analysed by transforming the system characteristic equation into the s-plane and then applying the well-known Routh–Hurwitz criterion.
A bilinear transformation is usually used to transform the left-hand s-plane into the interior of the unit circle in the z-plane. For this transformation, z is replaced by
The Routh–Hurwitz criterion states that the number of roots of the characteristic equation in the right hand s-plane is equal to the number of sign changes of the coefficients in the first column of the array. Thus, for a stable system all coefficients in the first column must have the same sign.
