| 引用本文: | 冯文希,罗飞,裴海龙,张先勇,段文勇.离散时滞Lur’e系统时滞依赖性稳定性判据[J].控制理论与应用,2021,38(10):1531~1541.[点击复制] |
| FENG Wen-xi,LUO Fei,PEI Hai-long,ZHANG Xian-yong,DUAN Wen-yong.Improved delay-dependent stability criteria for discrete-time Lur’e system with time-varying delays[J].Control Theory and Technology,2021,38(10):1531~1541.[点击复制] |
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| 离散时滞Lur’e系统时滞依赖性稳定性判据 |
| Improved delay-dependent stability criteria for discrete-time Lur’e system with time-varying delays |
| 摘要点击 2443 全文点击 731 投稿时间：2020-07-14 修订日期：2021-09-14 |
| 查看全文 查看/发表评论 下载PDF阅读器 |
| DOI编号 10.7641/CTA.2021.00447 |
| 2021,38(10):1531-1541 |
| 中文关键词 离散Lur’e系统 李雅普诺夫理论 线性矩阵不等式 稳定性 时滞系统 |
| 英文关键词 discrete-time Lur’e systems Lyapunov theory LMI stability time-delayed system |
| 基金项目 国家自然科学基金项目(61603325), 广东省自然科学基金项目(2018A0303130111), 广东省科技计划项目(2017B010117007, 201902020003)资助. |
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| 中文摘要 |
| 本文研究了离散时滞Lur’e系统的绝对稳定性和鲁棒绝对稳定性问题, 包含时变时滞和扇形有界约束的非
线性. 首先, 构造了新颖的李雅普诺夫-克拉索夫斯基泛函(Lyapunov-Krasovskii functional, LKF), 其中, 为了增补时
变时滞区间和其他系统状态变量之间的耦合信息, LKF中扩充了一些重要的向量. 其次, 结合改进的基于自由权重
矩阵求和不等式技巧, 推导了一些比已有结论保守性更低的绝对和鲁棒绝对稳定性判据. 稳定性判据保守性的减小
主要归功于改进的LKF和求和不等式技巧. 最后, 通过几个文献中常用的数值算例的求解仿真来说明本文判据的有
效性和先进性. |
| 英文摘要 |
| In this paper, the absolute stability and robustly absolute stability for discrete-time Lur’e systems with timevarying
delays and sector constraint nonlinearities are investigated. To begin with, an augmented Lyapunov-Krasovskii
functional (LKF) is designed, where some augmented vectors are chosen to complement some coupling information between
the delay intervals and other system state variables. Next, some improved delay-dependent absolute stability and
robustly absolute stability criteria are proposed via the modified LKF and a modified general free-matrix-based summation
inequality technique application. The proposed stability criteria can be easily solved by using the MATLAB linear matrix
inequality (LMI) toolbox. The stability criteria are less conservative than some results previously proposed. The reduction
of the conservatism mainly depends on the improvement of the LKF and the full use of the modified summation inequality
technique. Finally, some common numerical examples used frequently in some previous literature are presented to show
the effectiveness of the proposed approach. |
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