Generalization of the Concept of Pole-Zero Cancellation to Linear Time-Varying Systems

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 make an attempt to generalize the concept of pole-zero cancellation to linear time-varying systems. We firstly 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.