The phase margin (in degrees) of a system having the loop transfer function is $$G(s)H(s) = {{2\sqrt 3 } \over {s(s + 1)}}$$

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.

The system mode described by the state equations $$$X = \left( {\matrix{ 0 & 1 \cr 2 & { - 3} \cr } } \right)x + \left( {\matrix{ 0 \cr 1 \cr } } \right)u,y = \left[ {\matrix{ 1 & 1 \cr } } \right]x$$$