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基于状态分解的离散奇异时滞系统的容许性和$H_{\infty}$性能分析

1. 1. 安徽大学电气工程与自动化学院, 合肥 230601;
2. 计算智能与信号处理教育部重点实验室, 合肥 230601
• 收稿日期:2022-03-18 修回日期:2022-08-21 出版日期:2023-02-25 发布日期:2023-03-16
• 通讯作者: 智亚丽,Email:zhiyali87828@163.com
• 基金资助:
国家自然科学基金(62103001),安徽省教育厅高校自然科学重点研究项目(K120437022)资助课题.

LI Shujie, ZHI Yali, SUN Chengyu, SUN Xiantao. Admissibility and $H_{\infty}$ Performance Analysis of Discrete-Time Singular Systems with Time Delays Based on the State Decomposition[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(2): 271-280.

Admissibility and $H_{\infty}$ Performance Analysis of Discrete-Time Singular Systems with Time Delays Based on the State Decomposition

LI Shujie1, ZHI Yali1,2, SUN Chengyu1, SUN Xiantao1

1. 1. School of Electrical Engineering and Automation, Anhui University, Hefei 230601;
2. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Hefei 230601
• Received:2022-03-18 Revised:2022-08-21 Online:2023-02-25 Published:2023-03-16

This paper is concerned with the problem of admissibility and $H_{\infty}$ for discrete-time singular systems with time delays. Firstly, by decomposing the considered systems to differential-algebraic equations, the state decomposition method for continuous-time singular systems with time delays is expanded to discrete-time singular systems with time delays. The purpose is to construct a special Lyapunov functional whose the (double integral) quadratic forms are just composed of partial states and their related items. Then, the forward difference of the constructed Lyapunov functional is estimated by utilizing the summation inequality and the free matrix weighting approach, and thus a sufficient condition that can guarantee the considered systems with $H_{\infty}$ performance to be admissible is obtained. This condition has less conservatism and less computational burden, which is finally demonstrated by some numerical examples.

MR(2010)主题分类:

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