Given the characteristic equation $${s^3} + 2{s^2} + Ks + K = 0.$$ Sketch the root focus as $$K$$ varies from zero to infinity. Find the angle and real axis intercept of the asymptotes, break-away / break-in points, and imaginary axis crossing points, if any

The asymptotic approximation of the log-magnitude versus frequency plot of a minimum phase system with real poles and one zero is shown in Fig. Its transfer functions is

Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \right]x$$ the steady state value of $$\,\,{x_{ss}}\,\, = \mathop {Lim}\limits_{t \to \infty } x\left( t \right),$$ given the initial state value of $$x\left( 0 \right) = {\left[ {10 - 10} \right]^T},\,\,is$$

The output $$f$$ of the $$4$$- to- $$1$$ $$MUX$$ shown in fig. is