%0 Journal Article
%T EXPANSION OF SOLUTION TO A ROBOT MODEL WITH TIME DELAY<br>带时滞机器人模型解的展开
%A WANG Shuping
%A XU Genqi
%A ZHANG Guoshan
%A <br>王淑平
%A 许跟起
%A 张国山
%J 系统科学与数学
%D 2009
%I 
%X This paper is devoted to research of solution properties of a robot model with time delay, which is described by a retarded functional differential equations. At first the equations are transformed into an evolutionary equation in the Hilbert state space, and the well-posed-ness of the system is obtained by using the theory of $C_0$ semigroup. Then, by a detail spectral analysis, the asymptotic expression of all eigenvalues of the system operator is given, and it is shown that the eigenfunctions of the system operator fail to form a Schauder basis for the state space. However, it is proven that the solution of system can be explicitly expressed via its eigenvectors when $t>5\tau$, where $\tau$ is the delay time.
%K Robot model
%K time-delay differential equation
%K semigroup theory
%K spectral analysis
%K expansion of solution<br>机器人模型
%K 时滞微分方程
%K 半群理论
%K 谱分析
%K 解的展开.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=4AC03763139EAEAB0310FA13BDD0AAA7&yid=DE12191FBD62783C&vid=771469D9D58C34FF&iid=59906B3B2830C2C5&sid=9036AC33107DC7C4&eid=8D0822DF60ACC08F&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=30