分数阶系统的鲁棒稳定性研究
Study on the Robust Stability of Fractional-Order System
摘要: 本文将针对分数阶(α＞1)系统，同时考虑最常见的两种不确定类型，即多胞不确定和无穷范数。首先，给出了不确定分数阶系统无状态反馈时鲁棒稳定性条件。其次，采用线性矩阵不等式的形式给出了不确定分数阶系统状态反馈控制器的设计方法。最后，通过两个数值算例验证了理论的正确性。
Abstract: In this paper, we will consider the two most common types of uncertainty for fractional-order systems, which are subjected to poly-topic and H-infinity bounded uncertainties with (α＞1). Firstly, the robust stability conditions of uncertain fractional-order systems without state feedback are given. Secondly, the design method of state feedback controller for the fractional system with uncertainty is given in the form of linear matrix inequality. Finally, two numerical examples are given to verify the correctness of the theory.
文章引用：郭校中. 分数阶系统的鲁棒稳定性研究[J]. 动力系统与控制, 2022, 11(1): 19-26. https://doi.org/10.12677/DSC.2022.111003

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