Time-Response Characteristics of a System as Determined by its Transfer Function

Abstract

In this paper a study is made of the step and impulse responses of systems whose transfer functions have all their poles on the negative real axis. The effects that real zeros of the transfer function have on the system response are evaluated. One result shows that if the transfer function has <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> finite zeros, all on the positive real axis, then the step response of the system has exactly <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> zero crossings. These step-response characteristics are studied further to establish upper and lower bounds on the position of the zero crossing for the case <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 1</tex> , and other bounds on the time functions for the cases <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 0</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 2</tex> .