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Tabular method for determining root distribution of delta-operator formulated real polynomials

机译:确定增量算子公式实多项式根分布的表格方法

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摘要

A tabular method for the investigation of real polynomial root distribution with respect to the circle /spl verbar/c+1//spl Delta//spl verbar/=1//spl Delta/ in the complex plane is presented. Such a procedure is useful in stability considerations of /spl delta/-operator formulated discrete-time systems with sampling time /spl Delta/, in particular, when the characteristic polynomial contains literal coefficients. We show that, direct verification of stability may be preferable over techniques that utilize transformations when the sampling frequency is fast relative to the system bandwidth. In addition, as sampling frequency increases, the relationship with the well known Routh-Hurwitz table becomes apparent.
机译:提出了一种表格方法,用于研究相对于复杂平面中的圆/ spl verbar / c + 1 // spl Delta // spl verbar / = 1 // spl Delta /的多项式根分布。这样的过程在考虑具有采样时间/ spl Delta /的/ spl delta /-算子制定的离散时间系统的稳定性时特别有用,特别是当特征多项式包含文字系数时。我们表明,当采样频率相对于系统带宽较快时,直接验证稳定性可能优于采用变换的技术。另外,随着采样频率的增加,与众所周知的Routh-Hurwitz表的关系变得显而易见。

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