α{ \in }阶分数阶系统的Routh-Hurwitz稳定性和鲁棒稳定性判据[1，2]
Routh-Hurwitz criterion of stability and robust stability for fractional-order systems with order α{\in}[1,2)
摘要：
基于推广的Routh-Hurwitz判据，提出了一个判定阶为α{ \in }[1，2）的分数阶线性系稳定性的充分必要判据，称为分数阶Routh-Hurwitz判据.与已有的判据相比，该判据涉及的表达式更少、更简单，对分析分数阶不确定性系统的鲁棒稳定性具有重要意义。所有这些表达式都是关于系统矩阵特征多项式系数的显式表达式，因此可以直接描述分数阶不确定性系统的稳定参数区域。算例表明了该方法的有效性。
英文摘要：
Based on the generalized Routh-Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order α{\in}[1,2), called the fractional-order Routh-Hurwitz criterion. Compared with the existing criterion, our one involves fewer and simpler expressions, which is significant for analyzing robust stability of fractional-order uncertain systems. All these expressions are explicit ones about the coefficients of the characteristic polynomial of system matrix, so the stable parameter region of fractional-order uncertain systems can be described directly. Some examples show the effectiveness of our method.
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