(a) Consider a feedback system with (i) Write the closed-loop system function e...

(a) Consider a feedback system with

(i) Write the closed-loop system function explicitly as a ratio of two polynomials. (The denominator polynomial will have coefficients that depend on K.)

(ii) Show that the sum of the closed-loop poles is independent of K.

(b) More generally, consider a feedback system with system function

Show that if m ≤ n -2, the sum of the closed-loop poles is independent of K.