Module 3 : Stability Analysis of Discrete Time Systems

Lecture 2 : Stability Analysis using Bilinear Transformation and Routh Stability Criterion

Thus the Routh tabulation is continued as

As there is one sign change in the first column, one of the roots is on the right hand side of the w -plane. This implies that one root in z -plane lies outside the unit circle.

To verify our conclusion, the roots of the polynomial $ z^3 - 1.7
z^2-z+0.8=0$, are found out to be z = 0.5, z = -0.8 and z = 2. Thus one can see that z = 2 lies outside the unit circle and it is inverse of z = 0.5 which caused the all zero row in w -plane.