基于改进型离散Wirtinger型不等式的时变时滞系统稳定性分析

田海生; 龚德仁; 王楠; 段登平

Chinese

您当前的位置：

首页 >

文章列表页 >

基于改进型离散Wirtinger型不等式的时变时滞系统稳定性分析

更新时间：2026-09-04

- 基于改进型离散Wirtinger型不等式的时变时滞系统稳定性分析
- Stability analysis of time-varying delayed systems based on improved discrete wirtinger-based inequality
- 微电子学与计算机 2019年36卷第10期页码：21-26
- 作者机构：
  
  上海交通大学航空航天学院,上海,200240
- 作者简介：
- 基金信息：
  
  国家自然科学基金 61603249
- DOI：
  中图分类号：
- 纸质出版：2019
- 稿件说明：
移动端阅览
田海生, 龚德仁, 王楠, 段登平. 基于改进型离散Wirtinger型不等式的时变时滞系统稳定性分析[J]. 微电子学与计算机, 2019, 36(10): 21-26.

TIAN Hai-sheng, GONG De-ren, WANG Nan, et al. Stability analysis of time-varying delayed systems based on improved discrete wirtinger-based inequality[J]. 2019, 36(10): 21-26.
田海生, 龚德仁, 王楠, 段登平. 基于改进型离散Wirtinger型不等式的时变时滞系统稳定性分析[J]. 微电子学与计算机, 2019, 36(10): 21-26. DOI：

TIAN Hai-sheng, GONG De-ren, WANG Nan, et al. Stability analysis of time-varying delayed systems based on improved discrete wirtinger-based inequality[J]. 2019, 36(10): 21-26. DOI：

摘要

针对离散时变时滞系统的稳定性问题

采用改进型离散Wirtinger不等式方法进行研究

获得了一个保守性更低的稳定性判据.首先构造了一个新的辅助向量函数

利用正定矩阵的二次型都是正值的特性

提出了改进型Wirtinger不等式

获得了比传统的方法如离散Jensen不等式、离散Wirtinger不等式更好的求和逼近结果.在此基础上

构建了合适的Lyapunov-Krasovskii泛函

应用改进型离散Wirtinger不等式从而获得有更低保守性的稳定性判据

最终利用两个数值仿真完成验证.验证结果表明

利用新方法得到的时滞上界要大于现有的不等式方法

更接近理论值

从而表明了本文方法的有效性和优越性.

Abstract

In view of the stability analysis of linear discrete systems

an intense research has been conducted by adopting an improved discrete Wirtinger-based inequality. A new stability criterion of linear discrete systems with interval time-varying delay is derived

which yields less conservative stability conditions. By definition of a novel auxiliary function

we propose a better integral inequality and receive a tighter stability condition as compared to the recently results such as discrete Jensen inequality

discrete Wirtinger-based inequality. Based on the new inequality

we construct a dedicated Lyapunov-Krasovskii functional and obtain a tighter estimation of the derivative of Lyapunov-Krasovskii functional in terms of the new inequality. Finally

two numerical examples are given to demonstrate the efficiency of our new methods.

关键词

Keywords

references

KWON O M, PARK M J, PARK J H, et al. Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov-Krasovskii functional[J]. Journal of the Franklin Institute, 2013, 350(3): 521-540. DOI: 521

SEURET A, Gouaisbaut F. Wirtinger-based integral inequality: application to time-delay systems[J]. Automatica, 2013, 49(9): 2860-2866. DOI: 2860

ZENG H B, HE Y, WU M, et al. Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay[J]. IEEE Trans. Automat. Contr., 2015, 60(10): 2768-2772. DOI: 2768

NAM P T, PATHIRANA P N, TRINH H. Discrete Wirtinger-based inequality and its application[J]. Journal of the Franklin Institute, 2015, 352(5): 1893-1905. DOI: 1893

GAO H, CHEN T. New results on stability of discrete-time systems with time-varying state delay[J]. IEEE Transactions on Automatic Control, 2007, 52(2): 328-334. DOI: 328

ARIBA Y, GOUAISBAUT F. An augmented model for robust stability analysis of time-varying delay systems[J]. International Journal of Control, 2009, 82(9): 1616-1626. DOI: 1616

HE Y, WANG Q G, XIE L, et al. Further improvement of free-weighting matrices technique for systems with time-varying delay[J]. IEEE Transactions on automatic control, 2007, 52(2): 293-299. DOI: 293

FENG Z, LAM J, YANG G H. Optimal partitioning method for stability analysis of continuous/discrete delay systems[J]. International Journal of Robust and Nonlinear Control, 2015, 25(4): 559-574. DOI: 559

KWON O M, PARK M J, PARK J H, et al. Improved delay-dependent stability criteria for discrete-time systems with time-varying delays[J]. Circuits, Systems, and Signal Processing, 2013, 32(4): 1949-1962. DOI: 1949

HE Y, WANG Q G, LIN C, et al. Delay-range-dependent stability for systems with time-varying delay[J]. Automatica, 2007, 43(2): 371-376. DOI: 371

SUN J, LIU G P, CHEN J. Delay‐dependent stability and stabilization of neutral time‐delay systems[J]. International Journal of Robust and Nonlinear Control: IFAC‐Affiliated Journal, 2009, 19(12): 1364-1375. DOI: 1364

ZHANG X M, WU M, SHE J H, et al. Delay-dependent stabilization of linear systems with time-varying state and input delays[J]. Automatica, 2005, 41(8): 1405-1412. DOI: 1405

ZHANG B, XU S, ZOU Y. Improved stability criterion and its applications in delayed controller design for discrete-time systems[J]. Automatica, 2008, 44(11): 2963-2967. DOI: 2963

ARIBA Y, GOUAISBAUT F. An augmented model for robust stability analysis of time-varying delay systems[J]. International Journal of Control, 2009, 82(9): 1616-1626. DOI: 1616

MOON Y S, PARK P, KWON W H, et al. Delay-dependent robust stabilization of uncertain state-delayed systems[J]. International Journal of control, 2001, 74(14): 1447-1455. DOI: 1447

LI X, GAO H. A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis[J]. IEEE Transactions on Automatic Control, 2011, 56(9): 2172-2178. DOI: 2172

PARK P G, KO J W, JEONG C. Reciprocally convex approach to stability of systems with time-varying delays[J]. Automatica, 2011, 47(1): 235-238. DOI: 235

SAKTHIVEL R, MATHIYALAGAN K, ANTHONI S M. Robust stability and control for uncertain neutral time delay systems[J]. International Journal of control, 2012, 85(4): 373-383. DOI: 373

LIU K, FRIDMAN E. Wirtinger's inequality and Lyapunov-based sampled-data stabilization[J]. Automatica, 2012, 48(1): 102-108. DOI: 102

RAMAKRISHNAN K, RAY G. Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay[J]. Applied Mathematical Modelling, 2013, 37(3): 1468-1479. DOI: 1468

LIU J, ZHANG J. Note on stability of discrete-time time-varying delay systems[J]. IET Control Theory % Applications, 2012, 6(2): 335-339. DOI: 335

LEI B, SHENPING X, HONGBING Z, et al. Analysis on Robust Stability of Neutral Systems with Time-Varying Delay[J]. Journal of Hunan University of Technology, 2012, 1: 013. DOI: 013

ZHU X L, YANG G H. Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay[C]//American Control Conference, 2008. IEEE, 2008: 1644-1649.

SEURET A, GOUAISBAUT F. Integral inequality for time-varying delay systems[C]//Control Conference (ECC), 2013 European. IEEE, 2013: 3360-3365.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

超低功耗实时时钟电路的设计

V型沟槽SiC中子探测器的蒙特卡洛分析

大模型发展综述：从BERT到Deepseek的技术演进

低功耗设计的双链电源关断策略的实现与验证

基于多尺度融合与小目标增强的航拍车辆检测算法