The loop transfer function of a feedback control system is given by $$$G\left(s\right)H\left(s\right)=\frac{K\left(s+1\right)}{s\left(1+Ts\right)\left(1+2s\right)},\;K>0$$$ Using Routh-Hurwitz criterion, determine the region of K-T plane in which the closed-loop system is stable.

The gain margin of a system having the loop transfer function G(s)H(s) =$${{\sqrt 2 } \over {s(s + 1)}}$$ is

The asymptotic bode plot of the minimum phase open-loop transfer function G(s)H(s) is as shown in the figure. Obtain the transfer function G(s)H(s)

Consider a feedback system with the open loop transfer function given by $$G(s)H(s) = {K \over {s\left( {2s + 1} \right)}}.$$ Examine the stability of the closed-loop system using Nyquist stability.