%0 Journal Article
%T SIMULTANEOUS APPROXIMATE CONTROLLABILITY OF DOUBLE SYSTEMS WITH A COMMON INPUT FUNCTION<br>带有相同输入函数双系统的同时近似可控性
%A YANG Wei
%A LI Shengjia
%A <br>杨威
%A 李胜家
%J 系统科学与数学
%D 2010
%I 
%X This paper is concerned with the approximate controllability of two systems by means of a common input function. In the paper, the two systems are considered to be infinite-dimensional and one of them to be a Riesz-Spectral system. In this case, it is shown that if both systems are exactly controllable in time $T_0$ and the system generators have no common eigenvalues, then they are simultaneously approximately controllable in any time $T>T_0$. In addition, for special control operators, if one system $(A_1,B_1)$ is approximately controllable and the other$(A_2,B_2)$ is exactly controllable in time $T_0$, and the spectral sets of the two system generators satisfy the condition $\sigma(A_2)\subset \rho_{\infty}(A_1)$, then they are simultaneously approximately controllablein some time $T>0$. Finally, some applications of the obtained results are given and it is proved that the time at which the systems are simultaneously approximately controllable is optimal.
%K Linear system
%K Riesz-Spectral operator
%K simultaneous approximate controllability<br>线性系统
%K Riesz-spectral算子
%K 同时近似可控性.
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=0CD45CC5E994895A7F41A783D4235EC2&aid=EDF32A51D6CB6473B151F6E3881DA7EB&yid=140ECF96957D60B2&vid=340AC2BF8E7AB4FD&iid=5D311CA918CA9A03&sid=3F10405738B4D004&eid=14B92F3C984CB5EA&journal_id=1000-0577&journal_name=系统科学与数学&referenced_num=0&reference_num=12