When a unit ramp input is applied to the unity feedback system having closed loop transfer function $${{C\left( s \right)} \over {R\left( s \right)}} = {{Ks + b} \over {{s^2} + as + b}},\,\left( {a > 0,\,b > 0,\,K > 0} \right),$$ the steady state error will be

The range of K for which all the roots of the equation $${s^3} + 3{s^2} + 2s + K = 0$$ are in the left half of the complex $$s$$-plane is

The transfer function $$C(s)$$ of a compensator is given below: $$C\left( s \right) = {{\left( {1 + {s \over {0.1}}} \right)\left( {1 + {s \over {100}}} \right)} \over {\left( {1 + s} \right)\left( {1 + {s \over {10}}} \right)}}$$

The frequency range in which the phase (lead) introduce by the compensator reaches the maximum is

Consider the system described by the following state space representation
$$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet \left( t \right)} \cr {\mathop {{x_2}}\limits^ \bullet \left( t \right)} \cr } } \right] = \left[ {\matrix{ 0 & 1 \cr 0 & { - 2} \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] + \left[ {\matrix{ 0 \cr 1 \cr } } \right]u\left( t \right) \cr & y\left( t \right) = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] \cr} $$

If $$u(t)$$ is a unit step input and $$\left[ {\matrix{ {{x_1}\left( 0 \right)} \cr {{x_2}\left( 0 \right)} \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr } } \right],$$ the value of output $$y(t)$$ at $$t=1$$ sec (rounded off to three decimal places) is _____________.