This paper investigates the $H_{\infty }$ control problems of singular fractional-order interval systems with commensurate order $0<\alpha <1$. Firstly, novel conditions for the bounded real lemma in the sense of $H_{\infty }$ norm for nominal singular fractional-order systems are proposed, based on which the sufficient conditions for checking the admissibility and $H_{\infty }$ performance of singular fractional-order interval systems are derived. Secondly, the state feedback $H_{\infty }$ controller synthesis for singular fractional-order interval systems is addressed and the state feedback controller is designed. Thirdly, the dynamic output feedback $H_{\infty }$ controller synthesis for singular fractional-order interval systems is addressed and the dynamic output feedback controller is designed. Finally, three illustrative examples are given to show the effectiveness of the proposed results.

本文调查了 $H_{\infty }$ 相称奇数分数阶区间系统的控制问题 $0<\alpha <\mathrm{1个}$。首先，从意义上讲，有界实引理的新颖条件$H_{\infty }$ 提出了标称奇异分数阶系统的范数，在此基础上有足够的条件来检验可容许性和 $H_{\infty }$推导了奇异分数阶区间系统的性能。其次，状态反馈$H_{\infty }$研究了奇异分数阶间隔系统的控制器合成，并设计了状态反馈控制器。第三，动态输出反馈$H_{\infty }$研究了奇异分数阶间隔系统的控制器合成，并设计了动态输出反馈控制器。最后，给出了三个说明性的例子来说明所提出的结果的有效性。