【摘要】 研究了一类Lipschitz非线性系统降维观测器设计问题.得出了在同一条件下,可微Lipschitz非线性系统不仅存在全维观测器, 同时还存在降维观测器的重要结论.
【关键词】 非线性系统;降维观测器设计;Lyapunov函数
收稿日期:2014-02-11
*国家自然科学基金资助项目(11347112)
** 通讯作者,E-mail: chizimeng@126.com第4期一类Lipschitz非线性系统降维观测器设计 哈尔滨师范大学自然科学学报2014年第30卷0引言
关于非线性系统观测器设计方法应用最为广泛的一类是类Lyapunov方法.该类方法基于Lyapunov稳定性理论.基于类Lyapunov方法,很多人如Rajamani R和 Cho Y M[1], Besancon G和 Hammouri H [2]及 Dawson D M等[3], 对非线性部分满足Lipschitz条件的非线性系统的观测器设计问题进行了研究.该类系统可称之为Lipschitz非线性系统.该文亦对一类Lipschitz非线性系统进行了研究.相对于全维观测器, 构造降维观测器只需要较少的积分器, 因而也就使得整个反馈系统的结构较为简单.由此看来, 对非线性系统降维观测器设计进行研究具有实用意义,因而引起了广泛的关注[4-7].
1符号说明及研究背景
1.1定义如下符号
(1)(*)由对称引出的矩阵块;
(2)AT代表A的转置.
1.2研究背景
3结束语
首先在文献[8]已有结论的基础上, 提出了一种降维观测器设计的方法. 结合文献[8]的结论, 得出了在同一条件下, 可微Lipschitz非线性系统不仅存在全维观测器, 同时还存在降维观测器的重要结论.
参考文献
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[4]Boutayeb M, Darouach M. A reduced-order observer for non-linear discrete time systems. Systems & Control Letters, 2000, 39: 141-151.
[5]Garcia R A, D’attellis C. Trajictory tracking in nonlinear systems via nonlinear reduced-order observers. Int J Control, 1995, 62: 685-715.
[6]Stoorvogel A A, Saberi A, Chen B M. A reduced order observer based Controller design for opertimization. IEEE Transactions on automatic control,1994, 39: 355-360.
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[8]Zemouche A, Boutayeb M, Bara G I. Observers for a class of Lipschitz systems with extension to performance analysis. Syst Control Lett, 2008, 57: 18-27.
The Design of Reduced-Order Observer for a Class of Lipschitz Nonlinear SystemChi Zimeng, Wang Qiulin, Zhou Lei
(Tianjin University of Finance and Economics)Abstract:The problem of reduced-order observer design for a class of differential Lipschitz nonlinear system is investigated in this paper. In the same circumstance not only full-order observer but also reduced-order observer can be found for the differentiable Lipschitz systems.
Keywords: Nonlinear system; Reduced-order observer design; Lyapunov function
(责任编辑:黄永辉)