基于记忆型饱和控制器的非线性时滞系统的稳定性分析

doi:10.11772/j.issn.1001-9081.2024030406

《计算机应用》唯一官方网站 ›› 2025, Vol. 45 ›› Issue (4): 1349-1355.DOI: 10.11772/j.issn.1001-9081.2024030406

基于记忆型饱和控制器的非线性时滞系统的稳定性分析

葛超¹^,², 叶水清¹, 王红¹, 姚征¹()

^1.华北理工大学电气工程学院，河北唐山 063210
^2.北京星纪开元科技（唐山）有限公司，河北唐山 063210

收稿日期:2024-04-10 修回日期:2024-06-07 接受日期:2024-06-11 发布日期:2024-08-15 出版日期:2025-04-10
通讯作者: 姚征
作者简介:葛超（1980—），男，河北石家庄人，教授，博士，主要研究方向：时滞系统、神经网络、混沌系统采样控制
叶水清（1999—），男，湖北鄂州人，硕士研究生，主要研究方向：神经网络、非线性系统
王红（1980—），女，河北唐山人，讲师，硕士，主要研究方向：网络化控制系统
基金资助:
河北省自然科学基金资助项目(F2021209006)

Stability analysis of nonlinear time-delay system based on memory-based saturation controller

Chao GE¹^,², Shuiqing YE¹, Hong WANG¹, Zheng YAO¹()

^1.College of Electrical Engineering，North China University of Science and Technology，Tangshan Hebei 063210，China
^2.Beijing StarCentury Technology （Tangshan） Company Limited，Tangshan Hebei 063210，China

Received:2024-04-10 Revised:2024-06-07 Accepted:2024-06-11 Online:2024-08-15 Published:2025-04-10
Contact: Zheng YAO
About author:GE Chao， born in 1980， Ph. D.， professor. His research interests include time-delay system， neural network， sampling control of chaotic system.
YE Shuiqing， born in 1999， M. S. candidate. His research interests include neural network， nonlinear system.
WANG Hong， born in 1980， M. S.， lecturer. Her research interests include networked control system.
Supported by:
Natural Science Foundation of Hebei Province(F2021209006)

摘要/Abstract

摘要：

针对在记忆型饱和控制器的作用下，研究非线性时滞系统的指数稳定性问题。首先，考虑系统参数不稳定的因素；其次，利用包含分布式时滞项辅助反馈的多面体方法处理饱和非线性；同时，建立增广Lyapunov-Krasovskii泛函，并利用改进的积分不等式放缩积分项，从而导出基于线性矩阵不等式（LMI）的稳定性准则；此外，制定保守性较低的吸引域优化方案，以提高吸引域的上界；最后，通过一个仿真实例证明所提方案的有效性和实用性。实验结果表明，在非线性系统中，在相同的参数条件下，与无记忆型控制器的现有的吸引域优化方案相比，所提有记忆型控制器的吸引域优化方案具有较低的保守性。

关键词: 非线性时滞系统, 输入饱和, 增广泛函, 记忆型饱和控制器, 吸引域

Abstract:

Exponential stability of nonlinear systems with time delay under the action of memory-based saturation controller was studied. Firstly， the factors of system parameter uncertainty were considered. Secondly， the polytopic method with distributed time-delay term auxiliary feedback was used to deal with the saturated nonlinearity. At the same time， an augmented Lyapunov-Krasovskii functional was established， and the integral terms were scaled by the improved integral inequality， thus the stability criteria based on Linear Matrix Inequalities （LMI） were derived. In addition， an attraction domain optimization scheme with less conservativeness was developed to increase the upper bound of the attraction domain. Finally， a simulation example was given to prove the effectiveness and practicability of the proposed scheme. Experimental results show that compared with the existing attraction domain optimization scheme without memory-based controller， the proposed attraction domain optimization scheme with memory-based controller is less conservative.

Key words: nonlinear time-delay system, input saturation, augmented functional, memory-based saturation controller, attraction domain

中图分类号:

TP273

葛超, 叶水清, 王红, 姚征. 基于记忆型饱和控制器的非线性时滞系统的稳定性分析[J]. 计算机应用, 2025, 45(4): 1349-1355.

Chao GE, Shuiqing YE, Hong WANG, Zheng YAO. Stability analysis of nonlinear time-delay system based on memory-based saturation controller[J]. Journal of Computer Applications, 2025, 45(4): 1349-1355.

图/表 5

表1 不同方法在不同参数β下对应的吸引域上界

Tab. 1 Upper bounds of attraction domain of different methods with different parameters β

β	$P r o b . 1$ （本文方法）	$P r o b . 1'$ （文献［18］方法）
0.1	0.857 5	0.692 5
0.2	0.934 2	0.711 7
0.3	0.977 8	0.713 0
0.4	0.976 4	0.712 8
0.5	0.974 1	0.712 8

表1 不同方法在不同参数β下对应的吸引域上界

Tab. 1 Upper bounds of attraction domain of different methods with different parameters β

β	$P r o b . 1$ （本文方法）	$P r o b . 1'$ （文献［18］方法）
0.1	0.857 5	0.692 5
0.2	0.934 2	0.711 7
0.3	0.977 8	0.713 0
0.4	0.976 4	0.712 8
0.5	0.974 1	0.712 8

表2 不同方法在不同参数下τ对应的吸引域上界

Tab. 2 Upper bounds of attraction domain of different methods with different parameters τ

$τ$	$δ$	本文方法	文献［18］方法	文献［19］方法
0.1	1.0	0.994 8	0.988 0	0.985 8
0.2	1.0	1.069 2	1.062 0	1.005 1
0.3	2.4	0.649 9	0.615 2	0.599 1
0.4	2.4	0.561 2	0.557 9	0.524 8
0.5	2.8	0.346 6	0.342 0	0.338 5

表2 不同方法在不同参数下τ对应的吸引域上界

Tab. 2 Upper bounds of attraction domain of different methods with different parameters τ

$τ$	$δ$	本文方法	文献［18］方法	文献［19］方法
0.1	1.0	0.994 8	0.988 0	0.985 8
0.2	1.0	1.069 2	1.062 0	1.005 1
0.3	2.4	0.649 9	0.615 2	0.599 1
0.4	2.4	0.561 2	0.557 9	0.524 8
0.5	2.8	0.346 6	0.342 0	0.338 5

图1 例1不加控制时的状态响应曲线

Fig. 1 State response curve without control of example 1

图2 情况1~2加控制器后的状态响应曲线

Fig. 2 State response curves with controller under case 1 and 2

图3 例1中对吸引域估计

Fig. 3 Estimation of attraction domain in example 1

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基于记忆型饱和控制器的非线性时滞系统的稳定性分析

Stability analysis of nonlinear time-delay system based on memory-based saturation controller

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