A Generalization of Routh–Hurwitz Stability Criterion for Fractional-Order Systems with Order <i>α</i> ∈ (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 α∈1,2, called the fractional-order Routh–Hurwitz criterion. Compared with the existing criterion, ours involves fewer and simpler expressions, which is significant for analyzing the robust stability of high-dimensional uncertain systems. All these expressions are explicit ones about the coefficients of the characteristic polynomial of the system matrix, so the stable parameter region of fractional-order systems can be described directly. Some examples show the effectiveness of our method.

Keywords

• fractional-order systems
• generalized Routh–Hurwitz criterion
• robust stability
• high-dimensional systems