The Bode magnitude plot of the transfer function $$G\left( s \right) = {{K\left( {1 + 0.5s} \right)\left( {1 + as} \right)} \over {s\left( {1 + {s \over 8}} \right)\left( {1 + bs} \right)\left( {1 + {s \over {36}}} \right)}}$$ is shown below: Note that $$-6$$ $$dB/octave=-20$$ $$dB/decade.$$ The value of $${a \over {bK}}$$ is _______.

The frequency response of $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$ plotted in the complex $$\,G\left( {j\omega } \right)$$ plane $$\left( {for\,\,0 < \omega < \infty } \right)$$ is

The asymptotic approximation of the log magnitude vs frequency plot of a system containing only real poles and zeros is shown. Its transfer function is

The open loop transfer function of a unity feedback system is given by $$G\left( s \right) = \left( {{e^{ - 0.1s}}} \right)/s.$$
The gain margin of this system is