具有不可公度阶的一般分数阶线性定常系统渐近稳定性的一个判据
A criterion for asymptotic stability of general fractional-order linear time-invariant systems with incommensurate orders
摘要：
本文给出了阶数不协调的分数阶系统渐近稳定性的一个判据。现有的方法通常假设序参量为有理数或任意两个序的比值为有理数。在工程应用中，序参量往往是不确定的，可能是实数。进而确定了稳定参数区域的边界，将参数空间分解为有限个连通区域。所有参数属于同一区域的系统具有相同的稳定性。每个区域只需要检查一个点即可确定该区域的稳定性。本文所建立的方法具有较低的计算复杂性，并清晰地给出了序参数与稳定性的关系。一些例子说明了这种方法的优点。
英文摘要：
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational numbers. In engineering applications, order parameters are more likely to be uncertain which may be real numbers. Furthermore, the boundary of the stable parameter region is determined, which decomposes parameter space into the finite number of connected regions. All systems whose parameters belong to the same region have the same stability. Each region only needs checking one point to determine the stability of the region. The method established in this paper involves low computational complexity and clearly gives the relationship between order parameters and stability. Some examples show the advantages of this method.
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