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网络化非线性系统的非脆弱H∞控制

马卫国1,2,杨 忠2   

  1. (1. 南通大学电气工程学院,江苏 南通 226019;2. 南京航空航天大学自动化学院,南京 210016)
  • 收稿日期:2013-08-06 出版日期:2013-11-15 发布日期:2013-11-13
  • 作者简介:马卫国(1976-),男,讲师、博士,主研方向:网络化系统分析与控制;杨 忠,教授、博士生导师
  • 基金项目:
    国家自然科学基金资助项目(61005054, 61174065);高等学校博士学科点专项科研基金资助项目(20113218110013);江苏省产学研联合创新基金资助项目(BY2012018);南通市应用研究计划基金资助项目(BK2011041)

Non-fragile H∞ Control for Networked Nonlinear System

MA Wei-guo  1,2, YANG Zhong  2   

  1. (1. College of Electrical Engineering, Nantong University, Nantong 226019, China; 2. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)
  • Received:2013-08-06 Online:2013-11-15 Published:2013-11-13

摘要: 具有对数量化、网络诱导时延和数据包丢失的网络化Lipschitz非线性系统控制器,存在参数摄动问题。为此,设计一种加性非脆弱状态反馈H∞控制器。将数据量化和网络诱导时延对被控系统的影响,转化为系统的不确定参数,网络化控制系统建模为马尔可夫跳变系统。采用Lyapunov稳定性理论和线性矩阵不等式方法,给出网络化Lipschitz非线性系统的加性非脆弱状态反馈H∞控制器存在的充分条件,该非脆弱H∞控制器可通过解线性矩阵不等式求出。仿真结果表明,当控制器存在参数摄动时,与传统控制器相比,非脆弱控制器不仅能使被控系统稳定,而且满足设定的H∞性能指标。

关键词: 网络化非线性系统, 对数量化, 网络诱导时延, 数据包丢失, 非脆弱控制, 线性矩阵不等式

Abstract: The additive non-fragile state feedback H∞ controller is designed for networked Lipschitz nonlinear system with logarithmic data quantization, networked induced delay shorter than one sampling period and packet dropout governed by Markov chain subject to controller parameter perturbation. The effect of data quantization and network induced delay is converted the parameter uncertainties of the controlled system. The networked nonlinear system is formulated as a Markovian jump system. The sufficient condition of the additive non-fragile state feedback H∞ controller for the networked nonlinear system is derived in terms of linear matrix inequality based on Lyapunov stability theory. The H∞ controller can be obtained by the solution of linear matrix inequalities. Simulation results show that when there exit parameter perturbations in controller, the non-fragile controller can stabilize the controlled system and meet setting H∞performance index compared with the traditional one.

Key words: networked nonlinear system, logarithmic quantization, network induced delay, packet dropout, non-fragile control, linear matrix inequality

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