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Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation

机译：一类具有空间可变系数和非线性摄动的主从分布参数系统的鲁棒指数同步

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摘要

This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov's direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.
机译：本文研究了一类具有空间可变系数和时空可变非线性摄动的主从分布参数系统（DPS）的指数同步问题，该模型由几个半线性抛物型偏微分方程（PDE）建模。在局部Lipschitz约束下，扰动是时间，空间和系统状态的连续函数。首先，针对所有允许的非线性扰动，研究了非强迫半线性主从PDE系统的鲁棒指数同步的充分条件。其次，需要鲁棒的分布式比例空间微分（P-sD）状态反馈控制器，以使闭环主从PDE系统实现指数同步。利用李雅普诺夫的直接方法和零件积分技术，从空间微分线性矩阵不等式（SDLMIs）的角度给出了本文的主要结果。最后，提供了两个数值例子，说明了所提出的方法在带有非线性扰动的主从PDE系统的鲁棒指数同步问题中的有效性。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第11期|380903.1-380903.12|共12页
  • 作者

    Yang Chengdong; Qiu Jianlong; Yi Kejia; Chen Xiangyong; Zhang Ancai; Chen Xiao; Yang Liuqing;

  • 作者单位

    Prov Key Lab Network Based Intelligent Comp, Jinan 250022, Peoples R China.;

    Univ Rhode Isl, Dept Elect & Comp Engn, Kingston, RI 02881 USA.;

    Syst Engn Res Inst CSSC, Sci & Technol Underwater Acoust Antagonizing Lab, Beijing 100036, Peoples R China.;

    Linyi Univ, Sch Sci, Linyi 276005, Peoples R China.;

    Linyi Univ, Sch Automobile Engn, Linyi 276005, Peoples R China.;

    Prov Key Lab Network Based Intelligent Comp, Jinan 250022, Peoples R China.;

    Xi An Jiao Tong Univ, Sch Elect & Informat Engn, Xian 710049, Peoples R China.;

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