%0 Journal Article
%T Design of controllers and compensators for a serially connected string system and its Riesz basis<br>串联弦系统的控制器和补偿器的设计及其Riesz基
%A LIU Dong-yi
%A SHANG Ying-feng
%A XU Gen-qi
%A <br>刘东毅
%A 尚英锋
%A 许跟起
%J 控制理论与应用
%D 2008
%I 
%X Under free boundary conditions, for a serially connected string system with continuity of vertical force and discontinuity of displacement at the interior nodes, compensators are designed at the interior nodes to compensate the displacement, and controllers are placed on both endpoints to control the system. Thus, a closed loop control system is established. Its well-posedness is then shown via the semigroup theory. From spectrum analysis of operators, it is known that the spectrum of the system is composed of isolated eigenvalues with finite multiplicity, and its spectrum is located in a strip parallel to the imaginary axis in the left half complex plane. Hence, the existence of the Riesz basis is derived and the spectrum-determined growth condition is concluded. The asymptotic stability of the system is thus proved.
%K closed loop control systems
%K string system
%K feedback
%K control equipment
%K spectrum analysis
%K Riesz basis
%K asymptotic stability<br>闭环控制系统
%K 弦系统
%K 反馈
%K 控制设备
%K 谱分析
%K Riesz基
%K 渐近稳定性
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=970898A57DFC021F93AB51667BAED7F7&aid=07F085F8326909914FB93418A39FDE47&yid=67289AFF6305E306&vid=C5154311167311FE&iid=94C357A881DFC066&sid=07C52AC66061533A&eid=F2947E14627CD734&journal_id=1000-8152&journal_name=控制理论与应用&referenced_num=1&reference_num=9