Abstract This is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

中文翻译：

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离散积分器的分数阶评估。第二部分

摘要 这是我们之前论文 [19] 的延续（第二部分）。在本文中，我们提出了一种计算分数阶离散积分元分数阶值的简单方法。我们假设输入和输出信号是已知的。线性时不变分数阶差分方程被简化为变量 ν 中的多项式，其系数取决于测量的输入和输出信号值。人们应该解决线性代数方程或找到多项式的根。当测量的输出信号包含噪声时，这个简单的数学问题就会变得复杂。然后，多项式根是不稳定的，因为它们对系数可变性非常敏感。在论文中，我们表明离散积分器分数阶由于多项式的次数而非常僵硬。评估保证正确顺序的最小样本数。研究得到了一个数值例子的支持。