The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation e^-at u(t), a > 0 will be

Consider a unity feedback control system with open-loop transfer function $$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)}$$ . The steady state error of the system due to a unit step input is

The number of roots of $$s^3\;+\;5s^2\;+\;7s\;+\;3\;=\;0$$ in the left half of the s-plane are

The loop transfer function of a single loop control system is given by $$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \right)}}{e^{ - ST}}$$ Using Nyquist criterion, find the condition for the closed loop system to be stable.