Asymptotic properties of zeros for discrete-time linear systems with backward triangle sampled-and-hold using delta operator

Abstract

This article focuses on a well-studied theoretical problem that, for rapid sampling, a continuous-time system with minimum-phase properties may become a non-minimum phase discrete-time system in the discretization process. The properties of zeros for discrete-time linear models in the field of digital control when using the special shift operator was considered in this paper. From the former relevant studies one can know that the backward triangle sample-and-hold (BTSH) as an alternative hold method to discretize the continuous-time systems has an advantage over ZOH in stabilizing sampling zeros for linear system with classical forward shift operator. In this article, we deduce the exact sampled-data model of linear system using delta operator to replace forward shift operator in the case of BTSH. Furthermore, the expressions and properties of zeros for the corresponding discrete-time system are derived.