This article studies the problem of output feedback control for discrete-time systems with state multiplicative noises. Aiming at reducing the controller design conservatism, a novel finite frequency memory control approach is developed, which makes full use of both current and past output measurements together with the frequency spectrum information of disturbances. By augmenting the control input into the closed-loop system state, a descriptor system approach is proposed to facilitate the controller synthesis. Then, based on the Fourier transform, Parseval's relation, and Projection lemma, the linear matrix inequalities (LMIs)-based controller design results are obtained to guarantee the mean-square asymptotic stability with finite frequency performance for the resulting closed-loop system. The effectiveness of the developed approach is validated by an antenna motion control system.

中文翻译：

---

具有状态乘性噪声的离散时间系统的有限频率记忆输出反馈控制器设计

本文研究了具有状态乘性噪声的离散时间系统的输出反馈控制问题。为了减少控制器设计的保守性，开发了一种新颖的有限频率记忆控制方法，该方法充分利用当前和过去的输出测量以及干扰的频谱信息。通过将控制输入增加到闭环系统状态，提出了一种描述系统方法来促进控制器综合。然后，基于傅里叶变换、Parseval关系和投影引理，得到基于线性矩阵不等式（LMI）的控制器设计结果，以保证有限频率下的均方渐近稳定性由此产生的闭环系统的性能。所开发方法的有效性通过天线运动控制系统得到验证。