线性时滞系统区域极点配置的数值方法

作者：王 旭1,赵 江2 日期：2007-07-09/span> 浏览：4506 查看PDF文档

                                 线性时滞系统区域极点配置的数值方法
                                             王 旭1,赵 江2
（1.中国石化工程建设公司，北京 100101; 2.中国联合工程公司，浙江 杭州 310022）

摘 要：介绍了一种应用于线性时滞系统的区域极点配置的数值方法，它实质上是应用于线性定常无时滞系统的传统极点配置方法的推广应用。由于时滞系统的特征方程是超越方程，故有无穷多个特征值。该方法的目标是通过进行数值方法的不断迭代，来不断整合反馈增益阵，最终把最右端的一批极点配置到指定的区域中去。通过引入对带有输入迟延和状态迟延的线性系统进行配置的实例来对这一方法进行说明。实践证明，该配置方法能取得较好的配置效果。
关键词：时滞系统;状态反馈;区域极点配置

                Numerical method for Dpole placement of linear timedelay system
                                          WANG Xu1, ZHAO Jiang2
(1.Sinopec Engineering Incorporation, Beijing 100101, China; 2.China United Engineering Corporation, Hangzhou 310022, China)

Abstract: A/Dpole placement method for linear timedelay system to place the poles to a specified region was described, which extended the classical pole placement method for ordinary differential equations（ODE）. Since the characteristic equation is transcendental, it has infinitely many solutions. The target of the method is to place the several rightmost poles to a specified region through the iteration of the proposed numerical method. The method by means of the pole placement of a linear system in the presence of an input delay and a state delay was illustrated. The example demonstrates that the method can obtain good placement effect.
Key words: timedelay system; state feedback; Dpole placement

参考文献(Reference)：
［1］PEAUCELLE D, ARZELIER D. A new robust Dstability conditon for real convex polytopic uncertainty［J］. Systems and control letters,2000,40(1):21-30.
［2］MICHIELS W. Continuous pole placement for delay equations［J］. Automatica,2002,38(5):747-761.
［3］ENGELBORGHS K. Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations［J］. Advances in Computational Mathematics,1999,10(3-4):271-289.
［4］ENGELBORGHS K. DDEBIFTOOL v.2.00: a Matlab package for bifurcation analysis of delay differential equations［R］. Report TW 330,October,2001.
［5］MICHIELS W. An eigenvalue based approach for the stabilization of linear timedelay systems of neutral type［J］. Automatica,2005,41(1):991-998.
［6］MICHIELS W. Limitations of delayed state feedback: a numerical study［R］. Report TW 323, April,2001.
［7］PENG Dazhou, XU Bugong, GUO Yunzhi. αrobust stabilization for linear uncertain systems with multiple delays［J］. Control Theory and Application,2004,21(1):97-100.