For the block diagram shown in the figure, the transfer function $${{Y(s)} \over {R(s)}}$$ is

In the Nyquist plot of the open-loop transfer function

$$G(s)H(s) = {{3s + 5} \over {s - 1}}$$

corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at

Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are

$$G(s) = {1 \over {s - 1}}$$

The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is