Routh-Hurwitz criterion of stability and robust stability for fractional-order systems with order α∈[1,2)

2022/02/19 by Jing Yang, Yang, Jing, Xiaorong Hou +3
Engineering · Materials Science · Mathematics · #Advanced Control Systems Design #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Optical Materials Research

paper · pdf · doi:10.48550/arxiv.2202.09576

openalex publication_date 2022/02/19 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

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, 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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