In this paper, the problems of robust stability and stabilization, for the first time, are studied for delayed fractional-order linear systems with convex polytopic uncertainties. The authors derive some sufficient conditions for the problems based on linear matrix inequality technique combined with fractional Razumikhin stability theorem. All the results are obtained in terms of linear matrix inequalities that are numerically tractable. The proposed results are quite general and improve those given in the literature since many factors, such as discrete and distributed delays, convex polytopic uncertainties, global stability and stabilizability, are considered. Numerical examples and simulation results are given to illustrate the effectiveness of the effectiveness of our results.

中文翻译：

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具有凸多边形不确定性的延迟Caputo分数阶系统的稳定性和稳定性的新结果

本文首次研究了具有凸多边形不确定性的时滞分数阶线性系统的鲁棒稳定性和稳定性问题。作者基于线性矩阵不等式技术和分数阶Razumikhin稳定性定理，得出了解决这些问题的充分条件。所有结果都是通过数值上易处理的线性矩阵不等式获得的。由于考虑了许多因素，例如离散和分布的延迟，凸多面体不确定性，全局稳定性和稳定性，因此所提出的结果相当笼统，并且改进了文献中给出的结果。数值算例和仿真结果说明了我们的结果的有效性。