Extended Transfer-Function and Pole-Zero Cancellation in Linear Time-Varying Systems

Abstract

Pole-zero cancellation is a well-known and important concept in linear time-invariant systems. In contrast, transfer functions as well as poles and zeros are not defined for linear time-varying systems. In this paper, we attempt to generalize the concept of pole-zero cancellation to linear time-varying systems. We first introduce the new concept of extended transfer-function for linear time-varying systems in the time domain instead of the frequency domain. We then propose the computational procedure of pole-zero cancellation to linear time-varying systems. We finally discuss the meaning of the proposed computational procedure regardless of the lack of poles and zeros in linear time-varying systems. The proposed concept and computational procedure are illustrated by a numerical example.

Keywords

• pole-zero cancellation
• linear time-varying system
• kalman canonical decomposition
• minimal realization
• companion form