The state variable representation of a system is given as $$$\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 \cr 0 & { - 1} \cr } } \right]x;x\left( 0 \right) = \left[ {\matrix{ 1 \cr 0 \cr } } \right] \cr & y = \left[ {\matrix{ 0 & 1 \cr } } \right]x \cr} $$$

The response y(t) is

By performing cascading and/or summing/differencing operations using transfer function blocks G₁(s) and G₂(s), one CANNOT realize a transfer function of the form

For the signal flow graph shown in the figure, the value of $$\frac{\mathrm C\left(\mathrm s\right)}{\mathrm R\left(\mathrm s\right)}$$ is

A unity negative feedback system has an open–loop transfer function $$G\left(s\right)=\frac K{s\left(s+1\right)}$$.The gain K for the system to have a damping ratio of 0.25 is _____________.