The zero, input response of a system given by the state space equation $$$\left[ {{{\mathop {{x_1}}\limits^ \bullet } \over {\mathop {{x_2}}\limits^ \bullet }}} \right] = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]and\left[ {\matrix{ {{x_1}} & {\left( 0 \right)} \cr {{x_2}} & {\left( 0 \right)} \cr } } \right] = \left[ {\matrix{ 1 \cr 0 \cr } } \right]is$$$

A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has

The gain margin and the phase margin of a feedback system with G(s)H(s)=$${s \over {{{\left( {s + 100} \right)}^3}}}$$ are

The gain margin for the system with open-loop transfer function G(s)H(s)=$${{2(1 + s)} \over {{s^2}}}$$ is