The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown. Which of the foloowing statements is true?

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown. The gain and phase margins of G(s) for closed loop stability are

The magnitude plot of a rational transfer function G(s), with real coefficient is shown in figure. Which of the following compensators has such a magnitude plot?

Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]\,\,\,and\,\,\,{\rm B} = \left[ {\matrix{ p \cr q \cr } } \right],$$

where p and q are arbitrary real numbers. Which of the following statesments about the controllability of the system is true?