一类非线性中立型控制系统的绝对稳定性

广东工业大学学报 ›› 2007, Vol. 24 ›› Issue (1): 77-81.

一类非线性中立型控制系统的绝对稳定性

广东财经职业学院基础部广东广州510420；

出版日期:2007-02-01 发布日期:2007-02-01

Absolute Stability for a Class of Nonlinear Neutral Control Systems

(Department of Primary Courses,Guangdong College of Finance and Economics,Guangzhou 510420,China)

Online:2007-02-01 Published:2007-02-01

摘要/Abstract

摘要： 本文研究具有可变时滞的中立型Lurie控制系统的绝对稳定性.利用Lyapunov泛函方法建立了基于线性矩阵不等式的绝对稳定性条件,因而将稳定性条件的检验转化为数学软件Matlab线性矩阵不等式的求解问题.给出了定理条件下计算绝对稳定时时滞充分性上界的一个算法,数值例子表明了本文结果的有效性.

关键词: 中立型系统；绝对稳定；线性矩阵不等式； Lyapunov泛函；

Abstract: This paper deals with the absolute stability of a class of neutral Lurie control systems with time-varying delays.Some stability criteria in terms of matrix inequalities(LMIs) are obtained based on Lyapunov functional method,which is only to solve LIMIs for verifying the stability conditions.An algorithm is also presented to obtain a sufficient upper bound of delay for absolute stability.Two numerical examples illustrate the effectiveness of the proposed results.

Key words: neutral systems； absolute stability； linear matrix inequality； Lyapunov functional；

杨戈锋；. 一类非线性中立型控制系统的绝对稳定性[J]. 广东工业大学学报, 2007, 24(1): 77-81.

YANG Ge-feng. Absolute Stability for a Class of Nonlinear Neutral Control Systems[J]. Journal of Guangdong University of Technology, 2007, 24(1): 77-81.

参考文献

[1] Ju-HPark,,S Won.A note on stability of neutral delay-dif-ferential systems. Journal of the Franklin Institute Engineering and Applied Mathematics . 1999

[2] B Xu.Delay-independent stability criteria for linear continu-ous systems with time-varying delays. Internat J SystemsSci . 2002

[3] Ju-H Park,,S Won.A new delay-dependent criterion forneutral systems with multiple delays. Journal of Computational and Applied Mathematics . 2001

[4] B Xu.Stability of retarded dynamical systems:A Lyapunovfunction approach. Journal of Mathematical Analysis and Applications . 2001

[5] Y S Lee,,Y S Monn,W H K Kwon.Delay-depedent robustH∞control for uncertain systems with time-varying state-delay. Proceedings of the 40th SICE Annual Conference,July,2001 . 2001

[6] Ju-H Park.Stability criterion for neutral differential sys-tems with mixed multiple time-varying delay arguments. Math Comput Simul . 2002

[7] Popov V M,,Halanay A.About stability of nonlinear con-trolled systems with delay. Autom Remote Control . 1962

[8] J K Hale,M V Lunel.Introduction to Function DifferentialEquations. . 1993

[9] Somolines A.Stability of Lurie type functional equations. Journal of Differential Equations . 1977

[10] Ju-H Park,,S Won.Stability analysis for neutral delay-dif-ferential systems. Journal of the Franklin Institute Engineering and Applied Mathematics . 2000

[11] B Xu.Stability criteria for linear time-invariant systems withmultiple delays. Journal of Mathematical Analysis and Applications . 2000

[12] B Xu.Further results on the stability criteria of linear sys-tems with multiple delays. Journal of Mathematical Analysis and Applications . 2002

[13] Li-Ming Li.Stability of linear neutral delay-differential sys-tems. Bulletin of Australlian Mathematical Society . 1988

[14] B Xu.Stability criteria for linear systems with uncertain de-lays. Journal of Mathematical Analysis and Applications . 2003

[15] 魏俊杰,阮士贵. 中立型微分方程零解的稳定性与全局Hopf分支[J]. 数学学报. 2002(01)

[16] 甘作新,葛渭高. 一类时滞多非线性Lurie控制系统的绝对稳定性[J]. 数学学报. 2000(04)

[17] 年晓红. LURIE控制系统绝对稳定的时滞相关条件[J]. 自动化学报. 1999(04)

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed