Qualitative step response limitations of linear systems

Limitations are established on the step response of a system based on the location of the zeros in the region of convergence of its Laplace transform. It is shown that real zeros in the region of convergence of the Laplace transform for a class of functions of which rational and proper transfer functions are members influence the response by introducing sign changes in the response. This negativity is shown to lead to undershoot, overshoot and local extrema in the step response of the system. A necessary and sufficient condition for the response to exhibit a characteristic which is termed final overshoot is developed in terms of the number of real minimum-phase zeros in the region of convergence. Lower bounds on the overshoot exhibited by the response are also developed on the basis of the minimum-phase zeros in the region of convergence