Correct Answer - Option 4 : 0
Given that \({\rm{G}}\left( {\rm{s}} \right) = \frac{{\rm{K}}}{{{\rm{s}}\left( {{\rm{s}} + 1} \right)\left( {{\rm{s}} + 2} \right)}}\)
The characteristic equation is given as \(1 + {\rm{G}}\left( {\rm{s}} \right){\rm{H}}\left( {\rm{s}} \right) = 0\)
\(\therefore {{\rm{s}}^3} + 3{{\rm{s}}^2} + 2{\rm{s}} + {\rm{K}} = 0\)
For stability we have \(3 \times 2 > 1 \times {\rm{K}}\)
\(\therefore {\rm{K}} < 6{\rm{\;hence\;K}} = 0\)
