一类非线性中立型系统的渐近稳定性

journal6 ›› 2009, Vol. 30 ›› Issue (6): 11-17.

一类非线性中立型系统的渐近稳定性

（内蒙古师范大学数学科学学院，内蒙古呼和浩特 010022）

出版日期:2009-11-25 发布日期:2012-04-20

Asymptotic Stability on a Class of Nonlinear Neutral Systems

(Institute of Mathematics Science,Inner Mongolia Normal University,Huhhot 010022,China)

Online:2009-11-25 Published:2012-04-20
About author:BAO Jun-dong(1958-),male,was born in Inner Mongolian,professor,Dr.;research area is control theory of delay differential systems and stochastic delay differential systems.
Supported by:
Natural Science Foundation of Inner Mongolia Autonomous Region (200711020104)

摘要/Abstract

摘要：讨论了一类非线性中立型系统的渐近稳定性问题.引入了适当的向量Lyapunov-Krasovskii泛函，给出了不仅依赖于滞后项时滞，而且还依赖于中立项时滞的稳定性判据.改进了先前用于算子D中所施加的限制0<|α|<1.判定条件由LMIs给出，可以通过Matlab中的工具箱比较容易地进行求解.最后给出了数值仿真，以说明判据的可行性.

关键词： 渐近稳定性, 中立型系统, 时滞相关, 线性矩阵不等式

Abstract: This work gives a criterion for asymptotic stability of a class of nonlinear neutral differential systems.By
introducing suitable vector Lyapunov-Krasovskii functional,a delay dependent criterion which not only depends on the discrete delay but also on the neutral delay is presented.This paper has also broken away from the assumption of 0<|α|<1,which is used in the operator D in earlier report.The sufficient condition is expressed in terms of linear matrix inequality.In the end of the work,utilizing Matlab toolbox,the numerical simulation examples are presented to illustrate feasibility of the criterion.

Key words: asymptotic stability, neutral systems, delay dependent criteria, LMI approach

包俊东. 一类非线性中立型系统的渐近稳定性[J]. journal6, 2009, 30(6): 11-17.

BAO Jun-Dong. Asymptotic Stability on a Class of Nonlinear Neutral Systems[J]. journal6, 2009, 30(6): 11-17.

参考文献

[1] LU W S,LEE E B,ZAK S H.On the Stabilization of Linear Neutral Delay-Differential Systems [J].IEEE Transaction on Automatic Control,1986,AC-31(1):65-67.

[2] ZHANG Y,ZHAI D,LIU M,et al.Delay-Dependent Observer Design and Observer-Based Stabilization of Linear Neutral Delay Systems [J].Control Theory & Applications,2005,22(5):783-789.

[3] BAO J D.On State Feedback Regulator for Linear Neutral Systems [J].Chinese J. of Science Instrument,2008,29(8):304-308.

[4] CHEN J D,LIEN C H,FAN K K,et al.Criteria for Asymptotic Stability of a Class of Neutral Systems via a LMI Approch [J].IEE Proc-Control Theory Appl.,2001,148(6):442-447.

[5] PARK J-H,WON S.A Note on Stability of Neutral Delay-Differential Systems [J].Journal of the Franklin Institute,1999,336:543-548.

[6] KUANG Y.Delay Differential Equations with Applications in Population Dynamics [M]//Math. in Sci. Eng..San Diego:Academic Press,1993.

[7] BRARTON R K.Bifurcation of Periodic Solutions in a Nonlinear Difference-Differential Equation of Neutral Type [J].Quart. Appl. Math.,1966,24:215-224.

[8] KOLMANOVSKII V B,MYSHKIS A.Applied Theory of Functional Differential Equations [M].Boston:Kluwer Academic Publishers,1992.

[9] KOLMANOVSKII V B,MYSHKIS A.Introduction to the Theory and Applications of Functional Differential Equations [J].Kluwer Academic Dodrecht,1999.

[10] COPALSAMY K,LEUNG I,LIU P.Global Hopf-Bifurcation in a Neural Netlet [J].Applied Mathematics and Computation,198,94:171-192.

[11] EI-MORSHEDY H A,GOPALSAMY K.Nonoscillation,Oscillation and Convergence of a Class of Neutral Equations [J].Nonlinear Analysis,2000,40:173-183.

[12] AGARWAL R P,CRACE S R.Asymptotic Stability of Certain Neutral Differential Equations [J].Mathl. Comput. Modelling,2000,31(8/9):9-15.

[13] PARK J H.Delay-Dependent Criterion for Asymptotic Stability of a Class of Neutral Equations [J].Applied Mathematics Letters,2004,17:1 203-1 206.

[14] SUN Yuan-gong,WAMG Long.Note on Asymptotic Stability of a Class of Neutral Differential Equations [J].Applied Mathematics Letters,2006,19:949-953.

[15] NAM P T,PHAT V N.An Improved Stability Criterion for a Class of Neutral Differential Equtions [J].Applied Mathematics Letters,2009,22:31-35.

[16] GU K.An Integral Inequality in the Stability Problem of Time Delay Systems [C].Sydney,Australia:39th IEEE Conference on Decisiion and Control,2000:2 805-2 810.

[17] HALE J,VERDUYN LUNEL S M.Introduction to Functional Differential Equations [M].New York:Springer-Verlag,1993.