无穷维线性系统可控性的一个注记

A Note of Coctrollability of Infinite Dimensional Linear Systemy

设x和u是Banach空间．U*具有Radon-Nikodym性质［3］本文研究无穷维线性系统X(t)_=AX(t)=AX(t)十BU(t)的可控性．其中A和B是有界线性算子，我们证明：此系统在［O，T］上精确可控性的充要条件是存在正整教n，使得：其中，这是著名的有限线性系统可控性条件对无穷维系统的推广．

Let X and U be Banach Spaces and U* (the dualspaces of U) here theRadon-Nikoelym Property.In the Paper. We study the Controllability of the Iafinits dimensionalLinear systems.X(t) = Ax(t)+ Bu(t)Where x(t) A and B are bounded Linear operators. We Prove thatthe linear spstem is exactly eontrollable on if and only if there exists a positive integral nSuch thatWhere. range B. It is generalization of the controllability criterion for finite dimensional linearsystems