Although uniform reduction of the differentiators’ orders in the stable state-space integer order models yields in stable fractional order dynamics, stability may not be preserved by non-uniform reducing the orders of the involved differentiators. This fact causes that the powerful methods available for Lyapunov stability analysis of integer order systems cannot be easily applicable for stability analysis of the models obtained by non-uniform reduction of the orders (i.e., incommensurate order models). To overcome such a challenge, this brief aims to facilitate stability analysis of incommensurate order systems via finding whether stability of an incommensurate order system is deduced from the Lyapunov stability of its integer order counterpart. Applicability of this brief achievement is evaluated through stability analysis in some different case studies, such as the special case of linear time invariant systems, time–delay positive linear systems, Lotka–Volterra systems, and biological models.

中文翻译：

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动态系统中所涉及的微分子阶数和Lyapunov稳定性保持问题的非均匀归约

尽管稳定状态空间整数阶模型中微分器阶数的均匀减少产生稳定的分数阶动力学，但通过非均匀减少所涉及的微分器的阶数可能无法保持稳定性。这一事实导致可用于整数阶系统的李雅普诺夫稳定性分析的强大方法不能容易地适用于通过阶次非均匀归约获得的模型（即不公度阶模型）的稳定性分析。为了克服这样的挑战，本简报旨在通过查找是否从其整数阶对应物的 Lyapunov 稳定性推导出非公约序系统的稳定性来促进非公约序系统的稳定性分析。