Consider a discrete-time feedback system with (a) Sketch the root locus for K &...

Consider a discrete-time feedback system with

(a) Sketch the root locus for K > 0 and for K < 0.

(b) If you have sketched the root locus correctly for K > 0, you will see that the two branches of the root locus cross and exit from the unit circle. Consequently, we can conclude that the closed-loop system is stable for , where is the value of the gain for which the two branches intersect the unit circle. At what points on the unit circle do the branches exit from it? What is the value of ?