具有分布时滞的随机区间系统的鲁棒镇定

Journal of Systems Engineering and Electronics ›› 2009, Vol. 31 ›› Issue (10): 2464-2468.

具有分布时滞的随机区间系统的鲁棒镇定

苏春华^1,2, 刘思峰¹, 葛世龙¹

1. 南京航空航天大学经济与管理学院, 江苏, 南京, 210016;
2. 信阳师范学院数学与信息科学学院, 河南, 信阳, 464000

收稿日期:2008-06-25 修回日期:2008-09-20 出版日期:2009-10-20 发布日期:2010-01-03
作者简介:苏春华(1965- ),男,讲师,博士研究生,主要研究方向为不确定随机系统理论.E-mail:chslg@tom.com

Robust stabilization of stochastic interval systems with distributed-delay

SU Chun-hua^1,2, LIU Si-feng¹, GE Shi-long¹

1. Coll. of Economics and Management, Nanjing Univ. of Aeronautics and Astronautics, Nanjing 210016, China;
2. Coll. of Mathematics and Information Science, Xinyang Normal Univ., Xinyang 464000, China

Received:2008-06-25 Revised:2008-09-20 Online:2009-10-20 Published:2010-01-03

摘要/Abstract

摘要： 研究了具有分布时滞的随机区间系统的鲁棒镇定问题.利用区间矩阵的分解技术、Lyapunov-Krasovskii泛函及It公式,得到了该系统鲁棒镇定的时滞依赖的非线性矩阵不等式判据,进而给出了该系统在不同情形下鲁棒镇定或鲁棒稳定的时滞依赖的线性矩阵不等式(linear matrix inequality,LMI)判据.通过数值仿真说明了所得的LMI判别在实际应用方面的方便性和有效性.

Abstract: The robust stabilization of stochastic interval systems with distributed-delay is investigated.By employing the decomposition technique of interval matrixes,constructing Lyapunov-Krasovskii functional and using It's formula,a delay-dependent criterion for robust stabilization is obtained in term of nonlinear matrix inequalities.Furthermore,the delay-dependent criteria are proposed via linear matrix inequalities(LMI),which can be used to verify the robust stabilization or robust stability of this system under different cases.A numerical simulation shows the convenience and effectiveness of the presented LMI criterion.

中图分类号:

O231.3

苏春华, 刘思峰, 葛世龙. 具有分布时滞的随机区间系统的鲁棒镇定[J]. Journal of Systems Engineering and Electronics, 2009, 31(10): 2464-2468.

SU Chun-hua, LIU Si-feng, GE Shi-long. Robust stabilization of stochastic interval systems with distributed-delay[J]. Journal of Systems Engineering and Electronics, 2009, 31(10): 2464-2468.

参考文献

[1] Verriest E I.Stability and stabilization of stochastic systems with distributed delays[C]//Proc.of the 34th IEEE Conference on Decision and Control,1995:2205-2209.
[2] Florchinger P.Stability of some linear stochastic systems with delays[C]//Proc.of the 40th IEEE Conference on Decision and Control,2001:4744-4745.
[3] Verriest E I.Stochastic stability of a class of distributed delay systems[C]//Proc.of the 44th IEEE Conference on Decision and Control,and the European Control Conference Seville,2005:5048-5053.
[4] Eurich C W,Thiel A,Fahse L.Distributed delays stabilize ecological feedback systems[J].Physical Review Letters,2005,94(15):158104(4).
[5] Ficak B.Point delay methods applied to the investigation of stability for a class of distributed delay systems[J].Systems Control Letter,2007,56(3):223-229.
[6] Mao X,Koroleva N,Rodkina A.Robust stability of uncertain stochastic differential delay equations[J].Systems Control Letter,1998,35(5):325-336.
[7] Liao X X.,Mao X.Exponential stability of stochastic delay interval systems[J].Systems Control Letters,2000,7(2).307-328.
[8] Dong Y,Jian A F,Sang C W.Delay-dependent robust stability of stochastic uncertain systems with time delay and Markovian jjump parameters[J].Circuits Systems Signal Processing,2003,22(4):351-365.
[9] Chen W H,Guan Z H,Lu X M.Delay-dependent exponential stability of uncertain stochastic systems with multiple delays:an LMI approach[J].Systems Control Letters,2005,54(6):547-555.
[10] Wei G L,Wang Z D,Shu H S,et al.Delay-dependent stabilization of stochastic interval delay systems with nonlineardisturbances[J].Systems Control Letters,2007,56(10):623-633.
[11] 包俊东,邓飞其,罗倚.参数不确定分布时滞随机微分系统的指数稳定性[J].华南理工大学学报(自然科学版),2004,32(12):65-69.
[12] Wang Z,Liu Y,Fraser K,et al.Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays[J].Physics Letters A,2006,354(4):288-297.