Consider a linear and time-invariant system with a Transfer Function model given by

\[T(s)=\frac{N(s)}{D(s)}\]

(a) If a unit impulse signal is applied, demonstrate the implication of the location of the system's poles to the stability of the system.

(b) Extend the analysis and establish the conditions for stability for a general unity feedback closed-loop system depicted in Figure 4.84.

r(t) + e(t) C(s) d(t) G(s) 3F(4) + Figure 4.84 A general unity feedback control system. n(t)