The steady state solution of stable systems is due to simple poles in the jO axis of the s-plane coming from the input. Suppose the transfer function of the system is:
H_ (s)= (Y(s))/(X(s)) = 1/([(s+1)^2]+4))
Find the poles and zeros of H(s) and plot them in the s-plane. Find then the corresponding impulse response h(t). Determine if the impulse response of this system is absolutely integrable so that the system is BIBO stable.
Let the input x (t) = u (t). Find the y (t) and from it determine the steady state solution.