Consider the discrete-time unity feedback control system (with sampling period T = 0.2 second) whose open-loop pulse transfer function is given by:
G(z) = = K(z + 0.9)/z(z – 1)(z + 0.8)
Determine the range of values of the gain K for the stability of the system, using the bilinear transformation and the stability criterion of Routh-Hurwitz. Calculate the value of the critical gain (Kc) for which the system starts to become critically stable, as well as calculate the roots of the characteristic equation in this condition in the z-plane.