The steady-state solution of stable systems is due to simple poles in the jΩ ­axis of the s-plane coming from the input. Suppose the transfer function of the system is

(a) 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.

(b) Let the input x(t) = u(t) and the initial conditions be zero, find y(t) and from it determine the steady-state solution.

(c) Let the input x(t) = tu(t) and the initial conditions be zero, find y(t) and from it determine the steady-state response. What is the difference between this case and the previous one?

(d) To explain the behavior in the case above consider the following: Is the input x(t) = tu(t) bounded? that is, is there some finite value M such that |x(t)|

Transcribed Image Text:

Y (s) H(s) = (s + 1)? + 4 X(s)