ABSTRACT

This paper derives the bounded real lemma corresponding to $H_{\mathrm{\infty }}$ norm of the singular fractional-order system (SFOS). The $H_{\mathrm{\infty }}$ bounded real lemma established for both cases of $0<\alpha <1$ and $1<\alpha <2$ has no conservatism and it turns the original complex computation of $H_{\mathrm{\infty }}$ norm into linear matrix inequality (LMI) problem, which can be performed in a computationally efficient fashion. In addition, it can test the system stability automatically, which is critical for system analysis. From this advantage, the synthesis problem of $H_{\mathrm{\infty }}$ control for the SFOS is addressed in the form of LMI. The simulation study is performed to validate the effectiveness and efficiency of the proposed methods.

摘要

本文推导出对应的有界实引理 $H_{\mathrm{\infty }}$奇异分数阶系统 (SFOS) 的范数。这$H_{\mathrm{\infty }}$ 为两种情况建立的有界实引理 $0<\alpha <1$ 和 $1<\alpha <2$ 没有保守性，它变成了原来的复杂计算 $H_{\mathrm{\infty }}$将范数转化为线性矩阵不等式 (LMI) 问题，该问题可以以计算效率高的方式执行。此外，它可以自动测试系统稳定性，这对系统分析至关重要。从这个优点，合成问题$H_{\mathrm{\infty }}$SFOS 的控制以 LMI 的形式处理。进行仿真研究以验证所提出方法的有效性和效率。