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具有随机非线性和部分转移概率未知的马尔科夫系统的H_∞控制(英文) 被引量：5

H_∞ control for Markovian jump systems with incomplete transition probabilities and probabilistic nonlinearities
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摘要 本文研究了非线性马尔科夫跳变系统的H∞控制问题.研究上述系统时:1)利用了非线性的概率分布信息;2)利用了转移概率中已知部分和未知部分的关系.利用李雅普诺夫泛函方法和线性矩阵不等式方法,本文得到了使得系统随机稳定的充分条件并得到了相应的反馈控制增益.文中最后给出的例子表明了所建立模型和分析方法的有效性. This paper considers nonlinear H∞ control for Markovian jump systems.In considering the above mentioned systems we have made use of：1） the information of the nonlinear probability distribution; 2） the relationship between the known part and the unknown part of the transition probabilities.By using the linear matrix inequality technique,we obtained the sufficient conditions of stochastic stability for the systems and feedback gains for the H 1 controller based on the Lyapunov function method.A numerical example shows the effectiveness of the proposed modeling and the design approach.
作者 田恩刚 岳东 杨继全
机构地区 南京师范大学电气与自动化工程学院 南京邮电大学自动化学院
出处 《控制理论与应用》 EI CAS CSCD 北大核心 2014年第3期392-396,共5页 Control Theory & Applications
基金 supported by the National Natural Science Foundation of China(61273114,61273115) the Natural Science Foundation of Jiangsu Province of China(BK2012847,BK2012469)
关键词 随机非线性 部分转移概率未知 马尔科夫跳变系统 probabilistic nonlinearity partially unknown transition probabilities Markovian jump systems
分类号 TP13 [自动化与计算机技术—控制理论与控制工程]
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参考文献24

  • 1ZHANG L, LAM D J. Necessary and sufficient conditions for anal- ysis and synthesis of markov jump linear systems with incomplete transition descriptions [J]. IEEE Transactions on Automatic Control, 2010, 55(7): 1695 - 1701.
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同被引文献25

  • 1高飞,张洪钺.带马尔科夫参数时滞容错控制系统稳定性分析[J].北京航空航天大学学报,2006,32(5):566-570. 被引量：4
  • 2KAO Y G, WANG C, ZHANG L. Delay-dependent exponential sta- bility of impulsive markovian jumping eohen-grossberg neural net- works with reaction-diffusion and mixed delays [J]. Neural Process- ing Letters, 2013, 38(3): 321 - 346.
  • 3WU Z, PARK J H, SU H Y, et al. Stochastic stability analysis for discrete-time singular Markov jump systems with time-varying de- lay and piecewise-constant transition probabilities [J]. Journal of the Franklin Institute, 2012, 349(9): 2889 - 2902.
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  • 5KAO Y G, GUO J F, WANG C H, et al. Delay-dependent robust ex- ponential stability of Markovian jumping reaction-diffusion Cohen- Grossberg neural networks with mixed delays [J]. Journal of the Franklin Institute, 2012, 349 (6): 1972 - 1988.
  • 6YANG X S, CAO J D, LU J Q. Synchronization of randomly coupled neural networks with Markovian jumping and time-delay [J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2013, 60 (2): 363 - 376.
  • 7ZHANG H G, WANG Y C. Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays [J]. IEEE Transactions on Neural Network, 2008, 19(2): 366 - 370.
  • 8BOUKAS E K. Stochastic Switching Systems: Analysis and Design [M]. Berlin: Birkhauser Boston Inc, 2005.
  • 9WU Z G, SHI P, SU H, et al. Passivity analysis for discrete-time s- tochastic Markovian jump neural networks with mixed time delays [J]. IEEE Transactions on Neural Networks, 2011, 22 (10): 1566 - 1575.
  • 10MA Q, XU S Y, ZOU Y. Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities [J]. Neurocomputing, 2011, 74(17): 3403 - 3411.

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控制理论与应用
2014年 第3期

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