\text { A unity negative feedback system has loop transfer function } G(s)=\frac{0.25 K e^{-x}}{(s+1)(s+5)}, \text { where } K, T>0 \text {. } \text { Use the 1-1 Pade

approximation } e^{-x} \approx \frac{1-0.5 s T}{1+0.5 s T} \text { and the Routh-Hurwitz criterion to } determine the approximate range of K for stability as a function of T. Simulate the system in Simulink to confirm that your answer is approximately correct when T = 10°s, the response (to a step, just to be specific) must become unbounded as K increases above the critical value, and must be bounded and reach a final value (that you should compute) for K = 0.5 K* (one-half of the critical value for that value of T).(8 pts)