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Based on the generalized Routh-Hurwitz criterion, we propose a sufficient andnecessary criterion for testing the stability of fractional-order linearsystems with order {\alpha}{\in}[1,2), called the fractional-orderRouth-Hurwitz criterion. Compared with the existing criterion, our one involvesfewer and simpler expressions, which is significant for analyzing robuststability of fractional-order uncertain systems. All these expressions areexplicit ones about the coefficients of the characteristic polynomial of systemmatrix, so the stable parameter region of fractional-order uncertain systemscan be described directly. Some examples show the effectiveness of our method.

Routh-Hurwitz criterion of stability and robust stability for fractional-order systems with order {\alpha}{\in}[1,2)