This paper introduces an extension of the Mikhailov stability criterion to a class of discrete-time noncommensurate fractional-order systems using the nabla fractional-order Grünwald-Letnikov difference. The new stability analysis methods proposed in the paper are computationally simple and can be effectively used both for commensurate and noncommensurate fractional-order systems. The main advantage of the proposed methodology is the fact that the stability analysis of noncommensurate fractional-order systems leads to exactly the same computational complexity as for the commensurate-order ones. Simulation examples confirm usefulness of the proposed methodology.

中文翻译：

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一类离散时间非相称分数阶系统的修正Mikhailov稳定性准则

本文介绍了利用Nabla分数阶Grünwald-Letnikov差将Mikhailov稳定性准则扩展到一类离散时间不等分数阶系统。本文提出的新的稳定性分析方法计算简单，可以有效地用于相称和不相称的分数阶系统。所提出方法的主要优点是，非相称分数阶系统的稳定性分析会导致与相称阶系统完全相同的计算复杂度。仿真实例证实了所提出方法的有效性。