Input-output analysis of multirate feedback systems 论文

摘要

A general analytical technique described in this paper permits the extension of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> -transform methods to sampled-data systems containing synchronized switches which do not operate with the same sampling rate. Sampling periods of each switch are first expressed in the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T/p_{1} ... T/p_{n}</tex> (where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p_{1} ... p_{n}</tex> are integers not equal to zero) and then it is shown that each switch with a period <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T/p</tex> can be replaced by a system of switches and advance and delay elements where each switch operates with a sampling period <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> . In this way, the original sampled-data system can be represented by an equivalent system containing switches operating with the same sampling rate. The general solution of such equivalent systems is outlined in this paper.