The block diagram of a system is shown in the figure

If the desired transfer function of the system is $${{C\left( s \right)} \over {R\left( s \right)}}\, = {s \over {{s^2} + s + 1}},$$ then $$G(s)$$ is

Consider the system described by the following state space equations $$$\eqalign{ & \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 0 \cr 1 \cr } } \right]u; \cr & y = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] \cr} $$$

If $$u$$ unit step input, then the steady state error of the system is

Two monoshot multivibrators, one positive edge triggered $$\left( {{M_1}} \right)$$ and another negative edge triggered $$\left( {{M_2}} \right)$$ are connected as shown in figure.

The monoshots $${{M_1}}$$ and $${{M_2}}$$ when triggered produce pulses of width $${{T_1}}$$ and $${{T_2}}$$ respectively, where $${T_1} > {T_2}.$$ The steady state output voltage $${V_0}$$ of the circuit is

A $$3$$-bit gray counter is used to control the output of the multiplexer as shown in the figure. The initial state of the counter is $${000_2}.$$ The output is pulled high. The output of the circuit follows the sequence