具有非线性扰动的变时滞中立型系统鲁棒稳定性新判据

J4 ›› 2014, Vol. 36 ›› Issue (10): 2034-2040.

具有非线性扰动的变时滞中立型系统鲁棒稳定性新判据

惠俊军1,2，张合新1，孟飞1，张金生1，周鑫1

1（1.第二炮兵工程大学控制工程系，陕西西安 710025;2.陕西省宝鸡市150信箱11分箱，陕西宝鸡721013）

收稿日期:2012-10-26 修回日期:2013-06-25 出版日期:2014-10-25 发布日期:2014-10-25
基金资助:
国家自然科学基金资助项目（60904083）

A new robust stability criterion for neutral systems
with time-varying delays and nonlinear perturbation

HUI Junjun1,2 ,ZHANG Hexin1,MENG Fei1,ZHANG Jinsheng1,ZHOU Xin1

(1.Department of Automation,The Second Artillery Engineering University,Xi’an 710025;
2.P.O.Box 15011,Baoji 721013,China)

Received:2012-10-26 Revised:2013-06-25 Online:2014-10-25 Published:2014-10-25

摘要/Abstract

摘要：

研究一类具有非线性扰动的时变时滞中立型系统鲁棒稳定性问题。基于直接LyapunovKrasovskii泛函并结合自由权矩阵方法的分析方法，建立了线性矩阵不等式(LMI)形式的离散时滞和中立时滞均相关稳定性判据。与以往方法不同，在处理泛函导数时，该方法不包含任何模型变换和涉及交叉项的处理，只是通过引入相关项自由权矩阵，充分考虑各项之间的相互关系，降低了结论的保守性。最后，利用Matlab的LMI工具箱进行了的数值仿真, 算例仿真表明所提出的判据的有效性。

关键词: 中立系统, LyapunovKrasovskii泛函, 鲁棒稳定, 非线性扰动, 自由权矩阵, 线性矩阵不等式

Abstract:

The robust stability problem for neutral systems with time-varying delays and nonlinear perturbation is investigated. Based on the direct Lyapunov-Krasovskii functional approach and freeweighting matrix technology, neutral and discrete delay-dependent stability criteria for the system are formulated in terms of Linear Matrix Inequalities (LMIs). Unlike some existing methodologies, when dealing with the time derivative of Lyapunov-Krasovskii functional, the proposed approach involves neither model transformation nor dealing with the cross-term, and only introduces some freeweighing matrix for the correlation terms, in which the relationship between each terms is fully considered, and the less conservative robust stability criteria are proposed accordingly. At last, Matlab Toolbox LMI is used to perform some numerical simulations and the results demonstrate the effectiveness of the proposed stability criteria.

Key words: neutral system;Lyapunov-Krasovskii functional;robust stability;nonlinear perturbations;free-weighing matrix;linear matrix inequality

惠俊军1,2，张合新1，孟飞1，张金生1，周鑫1. 具有非线性扰动的变时滞中立型系统鲁棒稳定性新判据[J]. J4, 2014, 36(10): 2034-2040.

HUI Junjun1,2 ,ZHANG Hexin1,MENG Fei1,ZHANG Jinsheng1,ZHOU Xin1. A new robust stability criterion for neutral systems
with time-varying delays and nonlinear perturbation [J]. J4, 2014, 36(10): 2034-2040.

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