【摘要】 <正> 引言 在有限维场合,Kalman等在[1]中讨论了连续线性系统与其离散化系统的完全能控能观性之间的关系.在1978年的赫尔辛基会议上有人进一步研究了这个问题.文献[2]讨论了一般情形,得到了充分及必要条件.文献[3]进一步讨论了在Hilbert空间的有界控制系统的类似问题.本文将讨论控制是无界时的相应问题([4]第八章),推广了[3]的结果.更多还原

【Abstract】 In this paper, the relationship between the approximate unbounded controllabilityof a distributed parameter system x=-x+BU on the Banach space and its dis-crete system x_k+1=f（）x_k+g（）BU_k is given. It is proved that the system x=-x+BU is approximately controllable when its discrete system is approximatelycontrollable. Moreover, the inverse proposition is true if f and g satisfy certain condi-tions. A similar result about the unbounded observable problem also holds.更多还原