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

Abstract

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 {\alpha}{\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.