Question 13.8: Given T(z) = N(z)/D(z), where D(z) = z³ − z² − 0.2 z + 0.1, ...

Substitute Eq. (13.60) into D(z) = 0 and obtain³

z = \frac{s  +  1}{s  –  1}       (13.60)

s³ − 19s² − 45s − 17 = 0        (13.64)

The Routh table for Eq. (13.64), Table 13.3, shows one root in the right–half-plane and two roots in the left–half-plane. Hence, T(z) has one pole outside the unit circle, no poles on the unit circle, and two poles inside the unit circle. The system is unstable because of the pole outside the unit circle.

TABLE 13.3 Routh table for Example 13.8