Zeros are of extreme importance in linear systems theory, especially unstable zeros, which degrade achievable performance. Furthermore, the presence of a zero in a state-space model implies the existence of an initial condition and a nonzero input signal such that the output is identically zero; this property is called output zeroing. The purpose of this paper is to elucidate the properties of the zero dynamics within the context of input–output models, which, like state-space models, are time-domain models, but, unlike state-space models, have no internal state. In particular, the focus is on the zero dynamics of left polynomial fraction description (LPFD) input–output models whose denominator polynomial is not necessarily monic.

零点在线性系统理论中极其重要，尤其是不稳定的零点，它会降低可实现的性能。此外，状态空间模型中零的存在​​意味着存在初始条件和非零输入信号，使得输出相同为零。此属性称为输出归零。本文的目的是阐明输入-输出模型背景下的零动态特性，该模型与状态空间模型一样是时域模型，但与状态空间模型不同，它没有内部状态。特别是，重点是左多项式分数描述（LPFD）输入-输出模型的零动态，其分母多项式不一定是单数的。