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山东大学学报(工学版) ›› 2015, Vol. 45 ›› Issue (1): 54-63.doi: 10.6040/j.issn.1672-3961.0.2014.140

• 控制科学与工程 • 上一篇    下一篇

不确定随机多时滞系统鲁棒随机稳定性分析

张慧慧, 夏建伟   

  1. 聊城大学数学科学学院, 山东 聊城 252000
  • 收稿日期:2014-05-16 修回日期:2014-11-28 发布日期:2014-05-16
  • 通讯作者: 夏建伟(1978-),男,山东潍坊人,副教授,博士,主要研究方向为随机系统鲁棒控制.E-mail:jianweixia78@gmail.com E-mail:jianweixia78@gmail.com
  • 作者简介:张慧慧(1991-),女,山东临沂人,硕士研究生,主要研究方向为多时滞系统稳定性.E-mail:zhhly0217@163.com
  • 基金资助:
    国家自然科学基金资助项目(61004046, 61104117)

Robust stochastic stability for uncertain stochastic system with multiple delays

ZHANG Huihui, XIA Jianwei   

  1. School of Mathematics Science, Liaocheng University, Liaocheng 252000, Shandong, China
  • Received:2014-05-16 Revised:2014-11-28 Published:2014-05-16

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摘要： 研究了一类不确定随机多时滞系统的鲁棒随机稳定性问题,其中系统不确定参数满足线性分式结构。首先,将倒数凸方法加以推广,得到一个新的积分不等式引理;然后,充分考虑时滞区间上下限关系,构造了多时滞区间相关的李雅普诺夫函数,并在新的积分不等式方法下,得到具有更小保守性和较少自由变量的时滞相关稳定性条件; 最后,给出一些数值仿真实例,验证了所提方法的有效性。

关键词: 线性结构不确定性, 多时滞, 李雅普诺夫函数, 随机系统, 鲁棒随机稳定, LMI

Abstract: The problem of robust stochastic stability for a class of uncertain stochastic systems with multiple delays was investigated in this paper. The uncertainties were in linear fractional form. Firstly, a new integral inequlity lemma was derived by extending the reciprocally convex approach. Then, based on a multiple delay-interval dependent Lyapunov-Krasovskii constructed by fully considering the relationship between upper and lower time delay interval and the new integral inequlity approach, some novel delay-dependent stability criteria with less conservatism and less free weighting matrices were obtained. At last, some numerical examples were given to show the effectiveness of the proposed results.

Key words: linear fractional uncertainties, multiple delays, stochastic system, robust stochastical stability, Lyapunov-Krasovskii function, LMI

中图分类号: 

  • O231.3
[1] HE Y, WANG Q, LIN C, et al. Delay-rang-dependent stability for systems with time-varying delay[J]. Automatica, 2007, 43(2):371-376.
[2] YANG R, ZHANG Z, SHI P. Exponential stability on stochastic neural networks with discrete interval and distributed delays[J]. IEEE Transactions on Neural Networks, 2010, 21(1):169-175.
[3] PARK P, KO J, JEONG C. Reciprocally convex approach to stability of systems with time-varying delays[J]. Automatica, 2011, 47(1):235-238.
[4] WU Z, SHI P, SU H, et al. Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay[J]. Neurocomputing, 2011, 74(10):1626-1631.
[5] WANG C, SHEN Y. Improved delay-dependent robust stability criteria for uncertain time delay systems[J]. Applied Mathematics and Computation, 2011, 35(11):2880-2888.
[6] WU H, LIAO X, FENG W, et al. Mean square stability of uncertain stochastic BAM neural networks with interval time-varying delays[J]. Cognitive Neurodynamics, 2012, 6(5):443-458.
[7] CHENG J, ZHU H, ZHONG S, et al. Novel delay-dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations[J]. Applied Mathematics and Computation, 2013, 14(15):7741-7753.
[8] LEE W, LEE S, PARK P. Improved criteria on robust stability and H∞ performance for linear systems with interval time-varying delays via new triple integral functionals[J]. Applied Mathematics and Computation, 2014, 243(15):570-577.
[9] YU J. Novel delay-dependent stability criteria for stochastic systems with time-varying interval delay[J]. International Journal of Control, Automation and Systems, 2012, 10(1):197-202.
[10] HUA M, DENG F, LIU X, et al. Robust delay-dependent exponential stability of uncertain stochastic system with time-varying delay[J]. Circuits, Systems and Signal Processing, 2010, 29(3):515-526.
[11] ZHANG H, YAN H, CHEN Q. Stability and dissipative analysis for a class of stochastic system with time-delay[J]. Journal of the Franklin Institute, 2010, 347(5):882-893.
[12] LIU M, HO D, NIU Y. Robust filtering design for stochastic system with mode-dependent output quantization[J]. IEEE Transactions on Signal Processing, 2010, 58(12):6410-6416.
[13] ZHANG Y, HE Y, WU M. Delay-dependent robust stability for uncertain stochastic systems with interval time-varying delay[J]. Acta Atomatica Sinica, 2009, 35(5):577-582.
[14] DRAGAN V, MOROZAN T, STOICA A. Robust stabilization of linear stochastic systems[J]. Mathematical Methods in Robust Control of Linear Stochastic Systems, 2013, 52:381-436.
[15] XIA J, SUN C, ZHANG B. New robust H∞ Control for uncertain stochastic Markovian jumping systems with mixed delays based on decoupling method[J]. Journal of the Franklin Institute, 2012, 349(3):741-769.
[16] YANG H, ZHANG H, SHI H, et al. Robust H∞ fitering for uncertain nonlinear stochastic systems with mode-dependent time-delays and markovian jump parameters[J]. Circuits, Systems and Signal Processing, 2011, 30(2):303-321.
[17] ZHANG Y, WU A, DUAN G. Improved L2-L∞ filtering for stochastic time-delay systems[J]. Internatiomal Journal of Control, Automation and Systems, 2010, 8(4):741-747.
[18] BASIN M, RODKINA A. On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays[J]. Nonlinear Analysis: Theory Methods and Applications, 2008, 68(8):2147-2157.
[19] CHEN W, GUAN Z, LU X. Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: An LMI approach[J]. Systems and Control Letters, 2005, 54(6):547-555.
[20] BALASUBRAMANIAN P, KRISHNASNMY R, BKKIYAPPAN R. Delay-interval-dependent robust stability results for uncertain stochastic systems with Markovian jumping parameters[J]. Nonlinear Analysis: Hybrid Systems, 2011, 5(4):681-691.
[21] LI T, GUO L, LIN C. A new criterion of delay-dependent stability for uncertain time-delay systems[J]. IET Control Theory and Application, 2007, 1(3):611-616.
[22] WANG C, SHEN Y. Delay partitioning approach to robust stability analysis for uncertain stochastic systems with interval time varying delay[J]. IET Control Theory and Application, 2012, 6(7):875-883.
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