The robust asymptotic stability problem for fractional-order linear systems with commensurate time delays (FOSCDs) and structured perturbations is investigated in this manuscript. Based on the properties of Kronecker products and -analysis, the necessary and sufficient conditions are given to guarantee the asymptotic stability of FOSCDs. Then, the necessary and sufficient conditions for the robust asymptotic stability of FOSCDs with structured perturbations are investigated. To reduce the computing complexity and deal with the problems of systems with larger dimensions, a sufficient condition on the robust asymptotic stability of FOSCDs with structured perturbations is given based on the properties of Kronecker products and 2-norm transformations. Finally, several examples are illustrated to test the effectiveness of the proposed results.

中文翻译：

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具有相应时滞的分数阶系统的鲁棒渐近稳定性分析：1<β≤2 情况


本手稿研究了具有相称时间延迟（FOSCD）和结构化扰动的分数阶线性系统的鲁棒渐近稳定性问题。基于Kronecker积的性质和分析，给出了保证FOSCD渐近稳定性的充要条件。然后，研究了具有结构扰动的 FOSCD 鲁棒渐近稳定性的充要条件。为了降低计算复杂度并处理较大维系统问题，基于克罗内克积和2-范数变换的性质，给出了具有结构扰动的FOSCD鲁棒渐近稳定性的充分条件。最后，通过几个例子来检验所提出结果的有效性。