Tabular method for determining root distribution of delta-operator formulated real polynomials

A tabular method for the investigation of real polynomial root distribution with respect to the circle |c+1/Δ|=1/Δ in the complex plane is presented. Such a procedure is useful in stability considerations of δ-operator formulated discrete-time systems with sampling time Δ, in particular, when the characteristic polynomial contains literal coefficients. We show that, direct verification of stability may be preferable over techniques that utilize transformations when the sampling frequency is fast relative to the system bandwidth. In addition, as sampling frequency increases, the relationship with the well known Routh-Hurwitz table becomes apparent