Use Laplace transform and transfer function, we can do steady state analysis now for a system. Given a system model, we can find the transfer function. Further given the input, we can know the output response of the system at steady state (i.e., the response value when the time goes to infinity). Example:
−3 d³ y(t)/dt³ +2y(t)=du(t)/dt - Find the transfer function G(s) - If the input is u(t) (step signal), what is the output Y(s) - The steady state output y([infinity])= ?